Do symmetric positions have a higher draw ratio? From my experience in chess, I have observed that my draw ratio in symmetric positions (e.g. the Italian opening) is higher than in non-symmetric positions (e.g. the Spanish opening or different gambits). In general, do symmetric positions have a higher draw ratio?
Very good question, +1 from me.


  Is it true that asymmetric leads to win or lose and symmetric leads to draw?


It is not true that symmetric positions lead to a draw, and asymmetric ones to winning.

EXPLANATION:

Many people consider the Exchange variation of the Slav defense as drawn, but you will find that top grandmasters disagree.

In a symmetric position White has a small initiative or pressure, because he moves first.

The reason this gives drawn games is because even if White manages to make some advantage, it is usually small and it pins Black to defense "but that is all". Without a second weakness White can not win, and with proper defense he usually can not create it.

However, try to play symmetric position as Black against a stronger opponent and you will see just how hard it is to draw. The advantage of having permanent ( although small ) initiative or pressure counts a lot, and I am telling you this from my experience.

Although I do not play against humans that often, I regularly play against Shredder in my spare time. 

I always set the difficulty to hard and I always get "ground down" in the Exchanged Slav or in other semi-symmetrical positions-like 1.e4 e5.

I usually have an easier time drawing in asymmetrical positions, since the imbalance of strengths/weaknesses gives strong counter-play for both sides.

In the Queen's Gambit Declined-Exchange variation I usually draw way easier, although I do not know much of its theory.

The difference between symmetrical and asymmetrical positions is this:

In symmetric ones you have a small but permanent advantage as White. That means that you can win, draw or lose, while Black usually can only draw or lose. Here White needs to make an effort to outplay his opponent or else it will end as a draw. Hence in these positions a truly better player wins ( Black's position is harder to play, though).

In asymmetric positions both sides have strong counter-play so in these positions chances tend to be more equal. These positions are better for Black because you will have counter-play from the start while in the symmetric positions you will have to work very hard just to generate it-how many times did we all have "a won game" only to lose it because our opponent was "lucky to have that one saving tactical shot"?

Because asymmetric positions give greater chances for both sides to win you see them being more popular then symmetric ones. Also, they require less studying.

What I have noticed in the games of Karpov, Petrosian, Capablanca and many others is that they use simple positions that are objectively equal to outplay their opponents. 

Symmetric positions can serve great for this-your opponent thinks that it is a draw, but believe me when I say this, that extra tempo in the hands of the stronger and more creative player does count and can solve the game! I use this method too, and this method was used on me, so I speak from my experience.

Other players like Alekhin, Kasparov, Tal and so on, did not care for giving their opponents strong counter-play because they relied on their fantastic calculation strength.

Objectively speaking, if both play well, the game must end in a draw. It is a matter of choice how someone will fight for the win.

I prefer symmetric positions as White, since I am good at endgame and positional play, so to have a small but lasting advantage is enough for me. I will use my creativity to complicate the game and generate winning chances. These positions require a lot of creative work and high technique for both sides to be able to play them well.

As Black, I always play asymmetric lines because of the reasons given above ( believe me, it is not so easy to draw against Shredder relying on "sheer" strength even if the position is drawn! ). These positions require a strong calculating skill from a player and crafty use of tempo.

Hopefully this answer sheds some light and gives you some insight about strength / weaknesses of both types of positions.

EDIT IN RESPONSE TO THE COMMENT FROM MEMBER SalvadorDali:


  Also sentence like asymmetric positions require less time to study sounds really strange.


The beauty of the asymmetric position is the strength of the counter-play you get and how little energy and time it requires to find a plan. 

Let us compare two similar openings from Black's point of view-QGD and Slav-but let us focus on Exchange variations. 

[fen "r1bqrnk1/pp2bppp/2p2n2/3p2B1/3P4/2NBPN2/PPQ2PPP/R4RK1 w - - 0 1"]


In QGD it is easier to find a plan as Black-knight jump on e4, a6 or a5 pawn push vs minority attack or c4 outpost, "Petrosian knight", king-side piece attack and so on-you can think of a plan "right off the bat". Same goes for White-Nge2 plan, minority attack and so on. All this happens due to asymmetry. The counter-play is strong for both-if Black succeeds White loses, and same happens if White succeeds in carrying his plan out. Furthermore, you have limited amount of ideas to study. 

[fen "2r3k1/1prbbppp/pqn1pn2/3p4/3P4/P1NBPN2/1PRBQPPP/2R3K1 w - - 0 1"]


Now think about the Exchange Slav from Black's and White's point of view-can you offer a plan the same way? No you can not. This means that White will have to invest a lot of work to think of a plan that will give him more than a draw and that is not so easy to do in a nearly equal position. All you have here is an advantage of the first move which is enough for a small but lasting initiative but not for a win. However, in equal positions it is the strength and creativity of the both players that counts the most. One of the tries for White is to double rooks on the c-file and then enter voluntarily into IQP position. 

[fen "2r3k1/1prbbp1p/pqn1p1p1/8/3PQ3/P2B1N2/1PRB1PPP/2R3K1 w - - 0 1"]


This will make an endgame weakness but due to his slight initiative, and now space advantage, he will retain some chances to win. Again, he will need to be creative to be able to win so he nigh decide to "equalize the position" by opening the center thus transforming the position into open one, where he will have slight mobility advantage.
Still, that is just an initiative-Black can still defend- so White will have to transpose into a better endgame but that requires a lot more knowledge-especially since the position is equal-so the art of properly exchanging pieces will be crucial here. Let us say that White somehow manages to enter knight vs white bishop endgame-since the center is open and pawns are not fixed it will be hard for him to win. 

[fen "6k1/1p1b1p1p/p5p1/8/8/5N2/PP3PPP/6K1 w - - 0 1"]


He will again have to invest so much work in order to create winning chances, and will have to show inhuman technique so he can convert that advantage. 

As for Black, he must adapt to White's action, and if White is creative player, that means you need a lot of knowledge as well to parry his threats. And what about generating counter-play that gives you equal winning chances in the above diagram? Good luck with that! In symmetric positions it is only White who can win. 

What if I am 2550 ELO player with Black who plays against 2300 ELO White? If White knows his stuff he can draw easily-that is why GMs play the e6 move order instead of c6-QGD Exchange offers much easier play for a win. Think about the example for White I have described above, and tell me how would you generate winning chances? You will need an enormous amount of effort just to think of a plan, and high technique to carry it out. Not to mention the endgame technique required to outplay your opponent and convert the advantage. Same question for Black-how would you generate winning chances?

In symmetric positions-not only openings but middle and early endgames-you need a lot more work to generate tangible attack/counter-attack because everything is equal. You do not have a clear plan "right off the bat" and when you find one it is not as dangerous as it would be in the asymmetric position. 

That still does not mean that I should settle with a draw. But to win in such positions you need to have every aspect of your game at a high level because you never know where will you get the chance to outplay the opponent-in the middle game or endgame or maybe opening-and even when you get that chance you still get an advantage you must "grind down" and that also requires high level of technique.

In asymmetric positions you have it so much easier-you do not need every aspect of your game to be at the high level ( this is especially true for the endgame! ) to be able to outplay your opponent. You only need high tactical skill and good knowledge of the typical plans ( minority attack, knight jump to e4 and so on... ) and you are good to go. 

This brings me to the second part of your comment:


  Can you please clarify your experience a little bit deeper, I can understand such phrase from a GM, but sorry for my skepticism - but playing against computer program does tell nothing about your knowledge.


Although not so clear, I assume you think of this sentence:

Many people consider the Exchange variation of the Slav defense as drawn, but you will find that top grandmasters disagree.

Again, look at the example diagram for Exchange Semi-Slav and you shall see that only White can win. White has advantage of first move here and that really counts as he can unbalance the position first. He can change the position into Isolated Queen's Pawn or he can completely open the center. 

Black can only sit and wait. Although he is not weaker, he is passive and although computers have no problem drawing this position it is extremely hard for a human to just "soak up" punch after punch just to draw-come on Rocky Balboa at least won at the end! :)

That is why GMs tried to introduce an early Qb6 with Black in order to unbalance the position and get some counter-play or at least to get real winning chances after their positional suffering ends-the idea is to snatch a pawn on b2 and "suffer" until the endgame comes. Some abandoned the c6 move order completely and enter Semi-Slav this way:

[fen ""]

1.d4 d5 2.c4 e6!? 3.Nc3 c6


The point of this move order is to enter the QGD exchange variation instead of Slav exchange if White exchanges on d5.

I do not recall exactly the line in the Slav-I belong to those who abandoned the c6 move order and play e6 but here is the idea with Qb6:

[fen "rnb1kb1r/pp3ppp/1q2pn2/3p4/3P1B2/2N1PN2/PP3PPP/R2QKB1R w KQkq - 0 1"]


If you have additional questions leave a comment.

Best regards.