Ok, on my current memory card, I have all 6 F1 (NTSC) cars with over 900 miles each that have run the full 10 race distance of Formula GT in one shot each and each one has won the series, some with 8 victories, some with 9, but mostly 10 out of 10.
Each one entered the race series without oil changes. For the most part with practice its possible to win all the races in any given car. However, the races which you struggle to beat the AI in tend to be the Superspeedway and Test Course, especially in the F090/S because of the lesser HP. The F090/S is one of the most rewarding drives of the F1 fleet, as many people have already mentioned.
My biggest tip for beating the F1, as in F1 real life, is to treat every track differently. You'll need an entirely different downforce and gear ratio setting for each track, don't expect your test course setup to work well at Cote D'azur etc etc.
Take an experimental qualifiying lap after you make a change to your setup, to ensure that you're just about hitting the redline in 6th gear at the end of the longest straight on a particular track. If you're on an oval course use very little downforce, for Cote D'azur & Seattle use lots of downforce and for a track with a mix of tight corners and long flowing bends & straights use a little less than 1/2 downforce.
I find that a rearward brake bias helps, and I have not used any ASM or TCS for a long while now, although if its your 1st attempt at Formula GT, a couple of points on each won't hurt.
I'm by no means a "fast" F1 driver, I finished Cote D'azur in the F094/S last night, my fastest lap was 1'13.190 which is 10 or 12s slower than the fastest times by racers like 3rdgenracerx, (believe anything this guy says about GT3 F1 racing, 'cos he's probably right!) but I still finished 4 laps ahead of the 2nd placed F094/S.
Search through GTPlanet for setups for F1 cars, and most of all be patient. You really need to know your circuits and racing lines to be competitive in F1, a single spin can cost you a race here, so be confident that you can run 25 or more error-free laps. Spend some time in arcade mode free-run until you've refined the technique, then those AI F1s won't seem much of a challenge at all! (Except while you're lapping them!)