There are a few things that I don't like about it:
-can't hire based on stats (identical), neither class (randomly chosen after a mission).
-streamlined action system + class bonus instead of the pool of points from the original, weaker.
-"vigilance" means your people will open fire on first ennemy move, you can't decide whether to shoot or not, neither when. (Many times your guy opens fire before the ennemy is fully out of cover, which is STUPID. Also sometimes a far away ennemy gets out of cover and your guy shoots it with a shotgun, whereas you wanted him to shoot a closer ennemy should it show up...)
-can't hire engineers and scientists... (leading to next problem)
-3 missions at once giving you different bonus crew, that's a big pain in the ass, since engineers are critical (due to satellites and production), and so you may have to loose a country to get them. I don't think it adds to the game.
Not so sure about:
-Base side view, still wondering about why it changed.
-Single base, makes it simpler, but can't react to many UFO at once like in the original, different.
-interceptions, about the same as the original, it was a weak point of the original, a new take on it could have been welcome.
I'm playing classic mode, on my second game, abandoned the first as I did too many mistakes, might also give up on that one too as I didn't deploy enough satellites neither prioritized engineers.
The game is still addictive but the first point and occurence of the third make it very frustrating at times.
EDIT
Would *really* like:
-Remove % to hit, make that % of damage dealt, vary given range, cover and weapon.
Could be fun:
-Cooperative multiplayer, one base per player, one soldier per player when deployed in a mission (or something like that).