Ok the only game that is definately better is:
* Smash Bros Melee > Smash Bros
The ONLY thing I would change is to prehaps slow down the gameplay a tiny bit. The original is too slow by today's standards but I think Melee is a little too fast. I'd like to see a sequel find some middle ground in the speed department.
Games that are about the same:
* F-Zero GX = F-Zero X
F-Zero GX brings the awesome course design and 60FPS of F-Zero X but with outstanding graphics, lots of new modes and unlockables. But F-Zero X had much better music, the handling I liked a bit better and the X Cup.
* Wave Race BS = Wave Race 64
The games are quite different to each other which is part of the reason I like them about the same. The original game was extremely fun to play in Time Trial over and over again long after you beat the game due to the consistancy of the wave conditions.
However, the new game introduces more characters, different weather conditions, and a new control/handling system. Not that fun for time trial though.
* Mario Kart 64 = Mario Kart DD
I almost was going to say I liked 64 better but it's too close to tell. I much prefer the controls of the N64 game and the use of the hop/powerslide. DD just feels too dumbed down in this department.
N64's battle mode rapes DD's battle mode.
Racing is about the same. However I'm disapointed in DD that when you fall of the stage you don't fall onto a lower section and instead get transported back onto the track really quickly. Takes a lot of the fun out of it. Some of the best moments in the N64 game are things like trying to do massive shortcuts in Wario Stadium or Rainbow Road or make racers fall of the big jump in Wario Stadium or Royal Raceway.
I like DD's addition of character specfic items, the two character system and not being
able to hold items behind your kart to protect you and instead having to fire projectiles backwards to block incoming items/attacks.
I like the tighter, smaller course design in DD as it feels more like the SNES version in that you can see other racers more and interact and bump into them more.
1 player mode is far better in DD then 64. A.I. is much much better and doesn't cheat (well no where near as badly as the n64 version).
Having said all that though, if you gave me a remake of Mario Kart 64 with a rock solid 60FPS it would kick DD's arse!
Games that aren't as good as N64 versions.
* Super Mario 64 > Super Mario Sunshine
I actually went back and played both recently and it's a lot closer then I used to think. Mario 64 biggest strengths are its large number of stages and themes and better music. However, I like Mario Sunshine's hidden stages, increased difficulty, and those tight ropes just ROCK. Sunshine's "cleaning" sucks but I actually like the waterpack for it's other cool uses.
* Zelda: OoT + MM >>>> Zelda WW
Sorry but WW has the worst dungeon design in the series. OoT + MM's dungeons are FAR better then WW's which are really bland, have uninspired layout, and are really linear. Fighting would have been far better in WW then OoT and MM but the game is so gawd damn dumbed down in the difficulty/damage meter department that it ruins it.
* 1080 > 1080 avalaunche.
Even with only 6 courses in the original 1080, I find it better then the GCN one as the controls are just so much better. And the trick system is so dumbed down in Avalaunche. I do like the enviromental effects in Avalaunche and if the game had a few more stages like the very last stage (massive avalaunche) it would have been much better.
MAN I hope there are people that actually read this
EDIT: hopefully it's a bit easier to read.