Right now, for me, Scud Race is the harder of the two games. Well, that's probably because I played the heck out of Daytona 2 back in 02'-05' so it's more familiar to me.
I actually managed about a 3:48 on Expert and 2:56 on Advanced. I really don't know how I did it--you just have to play the heck out of the game and get used to every corner and hope you don't screw up. I'm not as good as I once was...it's hard to come in the Top 3 when playing at 100% speed.
Here are my tips for Daytona 2:
1. Get used to manual transmission. It really isn't that hard once you get a hang of it.
2. Do the fast start. This works for the 3 Daytona 2 cars (not the Hornet, see fast start in Daytona 1). Hold the brake and try to get the RPM's between the white & yellow parts of the tachometer (7000 RPM's). Then about .1 seconds before the guy says "Go," let off the brake and slam on the gas. You'll pop a wheelie and take off. Be careful that you don't rear-end the car in front of you (the lousy yellow SG8 Cartool car nonetheless) and make sure to upshift right away.
3. For most turns, I just slam the brakes and downshift from 4 to 2. Hold it in 2 until you get the car sideways. Then switch back to 4 and hit the racing line as normal. Try to brake slightly early so that you can compensate for the delay of having to overcome the forwards momentum. You can shift to 1st gear but it's very risky. I would only do it on really slow corners, such as the shipyard/factory area on Expert.

4. When powersliding, keep in the 4th gear. Your car regains speed faster while sliding than if you're in 3rd.
5. When shifting from 3rd to 4th gear, most tend to shift once the red light starts blinking. Don't shift then, wait until you get to about 290 kph (180 mph) until you switch to 4th. You get faster acceleration that way.
6. The natural tendency is to get the car to slide as far as possible without spinning out. While you can corner at a higher speed that way, if the slide is too far, it takes too long to straighten out and thus you hit the outside wall coming out of the turn. This is evident in most turns on Expert course since the tracks is not very wide. So take more moderate slides when necessary.
7. Draft as many cars as possible since the speed boosts are very potent in this game, even at the start of the race.
8. If you really suck, then just pick the Easy car (Chums Gum/JC Eagle) and don't get all fancy with the powerslides & stuff. Just play like you would Gran Turismo or Forza--hit the racing lines but play it safe. The car's high skidpad ratings should make it easy to get by.
That's about it--I may post more tips when I can think of them.