WARNING: Long post ahead. Forgive me if some of this is wrong, I'm going off the top of my head and I know some characters better than others.
Mario - F-smash and u-smash are buffed, pretty much the same aside from the loss of the tornado as a ground move. Still has issues with KOing.
DK - Pretty much the same, but the super armor frames help a bit. Still kinda slow, though.
Link - Range seems a tiny bit better, lost rapid-A combo, boomerang not as effective. Bombs got buffed, though. Up B recovery is little better. Clawshot is shorter than the Hookshot. :/
Samus - Some close range moves were nerfed and her projectile game got nerfed like CRAZY. F-air is scary good, though.
Bowser - Faster (a bit) and has a better side-B move. Power seems to be a little bit nerfed, though u-air is still a beastly killing move. Bowser bomb can function as anti-air now.
Yoshi - Egg Toss recovery is better than it looks. B-air is ridiculous. Range buffed but some moves were downgraded in terms of power. Eggs are slightly less flexible. Yoshi bomb hit on way up, too.
Peach - D-smash got NERFED TO HELL. U-air is usable now. Veggies not as useful since they disappear if blocked and are easy to catch. Second jump isn't even a jump. Still has amazing vertical killing prowess with u-air and u-smash. Side B has better range and is very useful now.
Luigi - Slower, f-air got nerfed. Has a lot of kill moves. N-air is buffed. Tornado and Luigiyuken are improved in terms of recovery. Luigiyuken combos out of jabs and kills at insanely low percentages.
Capt. Falcon - Slower, but still faster than most of the cast. Knee is harder to sweetspot. Falcon Punch can be turned around. side B is more useful for recovery since he doesn't stop if it hits someone.
Fox - Lost waveshine but picked up jump-cancelled shines that work almost the same way. Reflector is easy to spam and can be used to stall in mid-air. Blaster range is nerfed a bit. U-air and a-smash nerfed but are still powerful. B-air has no landing lag. Side-B lost some range.
Falco - Lots of moves changes. F-smash has some bad startup and lag but has excellent range. D-tilt nerfed. Side B spikes and has ridiculous range. Still jumps very high. Blaster can still be short-hopped. Reflector is a pseudo-projectile and can't be held out. Up B still sucks for recovery.
Zelda - Still slow but most moves have gained in speed, power and/or priority. Din's fire is probably best projectile in the game. Nayru's Love comes out fast. F-air and b-air kill at crazy low percentages when sweetspotted. F-tilt and u-tilt are excellent kill moves, f-smash and -u-smash do amazing damage. Overall, improved a LOT.
Sheik - Weaker, but still fairly quick. D-air is an auto-drop and harder to use due to lag and possiblity of SDing. Needles go downward whee thrown in the air. Has tether recovery. Up B can kill.
Kirby - Quicker in the air, moves are all improved in terms of range or power. Hard to kill due to new physics and his recovery. Hammer is more useful. Most moves don't require sweetspot to be effective anymore, like the aforementioned Hammer.
Jigglypuff - Pretty much the same aside from Stale Move Negation nerfing WoP aerials and Rest being nerfed a bit. Rest does do extra damage by putting a flower on your opponent's head. Slower on the ground, but still fast in the air.
Pikachu - Almost everything is better! He can chaingrab, Thunder is buffed, d-smash is nuts, f-smash is nuts, u-smash can be hyphen-cancelled... holy crap! :O
Marth - Mostly the same except neutral B is a stab and tipping is slightly harder. Side B is a LOT quicker, too.
Ice Climbers - Still a chaingrabbing monster, mostly the same as before. Projectile can be reflected by pretty much ANYTHING. Loss of wavedash means they have limited options for approaching. Up B can be used a tether recovery and Nana can grab the ledge if Popo is already grabbing it.
Ganondorf - U-smash is slightly different, side B is a grab, Warlock Punch can be turned around. U-tilt has vacuum effect. Otherwise, REALLY SLOW. Feels a lot slower and less mobile than in Melee.
G and W - Everything is pretty much better, though d-air is laggy even though it's pretty good compared to other auto-drop aerials.
Ness - Got some of his N64 power back. Aerials still rock. Has a high double jump still. Back throw is a monster. Still easily gimped during recovery. F-smash is a tad slower.
I would say most improved would either be Pikachu, Zelda or G&W, and most nerfed would be Sheik or Peach.
