Comparing the speed of the cars in the IL record for Aztec, first and second are using N64 EMU where as 3rd place is using a PS emu and the speed of the car looks to be a good 30 mph (or whatever speed they use) difference between the games.
I am gonna download the N64 emu to see if this is the case.
Honestly that would make sense, the N64 has a better processor, and if it's on an emulator the chances are that it will play smoother.
Just want to add a bit of clarity to this, as it hasn't really been addressed up to this point. The game does indeed run at different speeds based on region and console. Here are the different speed tiers, based on what I've noticed by watching videos and playing PAL N64.
PAL N64 200 max - 230 max single boost - 280 max charge boost This can be seen on my Aztec IL
NTSC N64/PS 175 max - 210 max single boost - ??? max charge boost This can be seen on Nimputs' Aztec IL
The top speed is also dependant on the track, as some allow for faster speeds than others. Here's an example:
Aztec: 200 max/175 max Ski: 191 max/168 max
Both N64 NTSC (Arbliterator) and PS PAL (Nimputs) have 168 max on Ski and Rally, so I'm making the assumption they run the same.
Time Trails always run at default speed, compared to Grand Prix which is influenced by the speed setting in the options menu. That's why chriswft has 200 max on Carbon Cup playing on PS, you can see he's playing at Master speed.
There's a big discrepancy between the IGT and the real time when playing on PS and N64 NTSC. Unlike N64 PAL which closely mirrors the actual time played, the IGT doesn't reflect the speed of the other two versions. This can be seen on Arbliterator's Rally IL, where he starts at ~0:09 and finishes at ~1:53 with a time of 2:04:36. The same goes for Nimputs' Aztec IL, which starts at ~0:04 and finishes at ~3:02. This also applies to Grand Prix, as Chris finishes with a IGT time of 3:23:28, even though his timer says 2:45.0.
As for breaking and drifting, I can't really comment as I haven't played both versions. I do know that on PAL N64 I'm constantly tapping the break button when cornering and some of the tracks just wouldn't be possible without doing so. Whether it's easier to corner on PS or not, I can't say.
Oh just to add, I'm not playing on an emulator. Though based on what I've seen of Rubii's Aztec IL it looks like they run pretty similarly.
So in short: PAL N64 is best for Time Trial, NTSC N64/PS is best for GP.