Which one is more important between endgame studies and tactics? One strong player once told me that you can improve quickly if you focus more on endgame studies than on tactics training. His reasoning was that endgame studies use a few pieces to cover most of the chess rudiments including strategy, tactics, imagination, concrete calculation, awareness, visualization, etc. While tactics on the other hand can lead to speculation over calculation. 

My question is, can a player improve quickly by focusing more on solving endgame studies and giving tactics less time?
Endgame studies are a particular form of tactical problem. I think variety is always good here, but, most importantly, since consistency is critical for improvement at chess, I would suggest you to focus on the type of exercise you enjoy most! (You won't train for too long if it's a sacrifice rather than a pleasure.)

I disagree with the "tactics can lead to speculation" part. Quite the opposite, training tactics is what we do to find concrete realizations of our intuitions/speculations. Of course, this means trying to calculate the entire continuation from the starting position, with all the possible consequences of the moves you are thinking about being considered. But this also applies to solving endgame studies, though!

Finally, I'd say that endgame studies seldom cover relevant strategy, and when they do, it's in a very artificial form. Anyway, if we wanted to improve our chess strategy, why not study chess strategy itself?

In conclusion, I think endgame studies can help you improve your tactical skills, but I'd use them as an additional resource rather than the main focus of your training. Tactical puzzles often have the advantage of being closer to positions you can reach in a real game (you are forced to "remove the noise" and find what's the relevant factor that can lead you to a win.) This does not mean that you should disregard the Master's advice, but rather stick to what's useful from it, so: beware of speculation during your tactical training!