Does the Bible say that it is better to have been born after Christ? I have often imagined living as a Jew before Christ and can never really hold the thought that I would enjoy it that much. At first it seemed like a bit of a poor attitude on my part, but then I thought maybe it is just that life seems so much better after Christ? This leads me to a more formal theological question.  'Does the Bible say that it is better to have been born after Christ?' If it is better after Christ, in what specific ways?

Note: When I say as a Jew before Christ, I am imagining myself back then so that it is 'a believing Jew', who believed in the coming Christ and inherited eternal life just as those born after.
I will take a stab at this question, and say "Yes" the Bible does teach that it is better, but I caution not reading "better" as meaning "more pleasant," as your question included the statement that you would not have "enjoyed" Judaism much. Instead, it is better for some very specific reasons.  

When I read your question, my mind instantly went to Hebrews, because the book of Hebrews is saturated with the idea of "better."  As a Son, Jesus is in a better position than the angels.  Our gospel is better than the sacrificial system. We have a better Sabbath, a better High Priest, and a better sacrifice.  It sounds odd to say, but Hebrews six and eight convey the idea that our position in Christ is founded on better promises. I don't fully grasp how the promises of God get "better" but Hebrews tells us that they do. We also know from Hebrews that we have a better hope and a guarantee of a better covenant (7:19-22). Other ideas in Hebrews include a better country, better resurrection, a better mediator, better blood.

So, yes, in seeing the comparison between before and after Christ, Hebrews seems to be the most comprehensive answer to your question, and the answer it gives is a resounding "Yes!" I believe  Hebrews is addressing a situation in which Jewish Christians were continuing to participate in temple worship, with all of its rites and ceremonies. They insisted on practicing circumcision, making the sacrificial offerings, and were essentially trying to Judaize their Christian faith. Why pour low octane fuel into your old Yugo when you have a Ferrari sitting here the runs on jet fuel?  That's better!