For most franchises I just don't see much point. But here are a few of my own picks.

Wave Race 64 > Wave Race Blue Storm. I just couldn't get into Blue Storm. The controls give me issues--I feel like either the riders struggle with turning or they turn too easily, never just right. That and the music and announcer chatter isn't as good as 64, in fact each rider has their own announcer, which means some riders I can actually control (like the australian guy) I prefer not to play as because I find their announcer annoying.

Moto Racer > Moto Racer 2. This one I just have a harder time defining, but the original Moto Racer feels like a really strong, well put together game, but somehow its sequel, while still fun, doesn't feel quite as "just right" despite having more features.

And since I'm mainly talking racers here, none of the future Mario Karts have ever felt as good as the original SNES one to me.

One more:

Marvel vs Capcom 1 > Marvel vs Capcom 2. 2 would be the clear superior if it weren't for two things: First, the ridiculous points/shopping method for unlocking characters and second, the music sucks. The first one doesn't have either of these issues.