Based solely on the known events of the first film I don't see why the TNG crew as individuals would necessarily be that different, though of course whether they all end up together and what their ship would look like have probably been altered. That said, it's certainly possible that differences could exist, especially if any of them had ancestors on any of the ships shown in the first film.
The existence of a human being depends on a very specific set of circumstances. Change any one of these things and you will greatly alter history, such that it is extremely unlikely that this same person will exist in the same way. Remember: butterfly effect.
Let's take Picard, for example. The reason he is who he is, is because his parents met at a very specific time, married, produced him and Robert, etc. Now it is true that the divergence of timelines took place long before either of these men were born. Their parents could have been alive at the time, but let's assume they weren't. Who's to say that any of the Picard grandparents even met in the Abramsverse? Nero's attack on Earth could have delayed Grandpa's shuttle flight, so that he never meets Grandma, etc. Now do you see what can happen?
And even if the Picard ancestors all meet and produce the children they originally did, who's to say they'll be the same? Perhaps in the new timeline, some of these couples decide to have children earlier (i.e. nuChekov) or later. Perhaps they have daughters instead of sons. Etc. etc.