Had a chance to play each stage, a few thoughts while it's fresh in my head.
You can now button config while in-game! And the button config is now greatly improved, as it tells you what the button you're setting DOES instead of just giving you a picture of an XBOX 360 controller... however, only the in-game button config is the new improved one, if you try to change buttons from the main menu it's the old shitty one. Weird but as long as a good one exists I don't really care.
Double tap to dash exists and also it's optional so you can turn it off (which I did because I hate that shit lol). There were other new options that I didn't really investigate but they seemed related to the fanfare when you absorb an enemy, like you could turn stuff off that previously had always been on. I don't see myself changing those settings.
Some bugs were fixed. Most of these were... bugs that I kinda could have lived without them being fixed. For example there was a bug I found where if you get hit while climbing up a box, you take damage and get temporary invulnerability but you wouldn't go into hitstun. Now that's fixed and you go into a LOT of hitstun, which negates a little timesaving trick I had found. There was another bug where if you dashed into the the right spot on a ledge you would clip to the the top of the ledge instead of hanging, now if you touch a ledge at all you always get that hanging animation. I guess I understand these things being changed but I don't really like it. On the other end the one bug I really wanted fixed, which was framerate loss in two specific parts of Water Works, is still present.
You're no longer obligated to learn how to play the game every time you boot it up! That's good!
Uh, there is a LOT more loading time now, dunno what's up with that, but it is REALLY noticeable any time you die. Not great.
The balance changes are mostly really subtle. It's every so often I was just like wait why's that guy there and I'd dash straight into an enemy or something. One change I really like is the little floor washing guys are gone from Power Plant. It used to be there would be one that would trap you in a small corridor and you would either have to fight it or get hit on purpose (I would always get hit). Now there's just one of the little worker guys and he's further from that corridor so you can just go right past him. The minibosses are another place it's noticeable, they take a few less hits to kill which is very welcome.
Look at this image:
http://i.imgur.com/NNr5R7I.jpg
You can stand here now. When the game first came out you could stand here, then it was changed so that you're weirdly hovering off the ground and would eventually fall into the spikes. Now you can stand here again. I guess when they changed it last time it was an accident (or changing it THIS time is an accident). In any case it makes getting this shortcut much easier.
There's a lot of other little changes but that's the stuff that stands out to me.