To cut a long story short, I have been playing FM3/GT5 recently with a controller (Normally use a wheel), and I can relate to the OP's situation.
The issue is you are 'tapping' the controller to turn small amounts, in FM3, this is taken as a large/sudden input and will cause a lot of cars to obviously misbehave.. In GT5, the tap is heavily filtered so it doesn't have much effect on the car.
If this is what you are experiencing, then depending on which side of the fence you reside on will depend on which game you think is 'broken'.. in FM3, you have to use the stick as analogue, and if you want small corrections, then just use very small taps. In GT5, you can make big taps to change direction as it's clearly designed to also be played using the D-Pad, and there is the most obvious diffference IMO.
I would say that put some time in to learn using the pad in a proper analogue manner, but then when you hop back to GT5, it'll feel wrong again.. So I'd agree with others, if you want to use a more (dare I say 'arcade') method of digital steering with FM3, just turn the stability control on..
As for the AI, I know the feeling, if you brake too early, they are as dumb as any other game and invariably ram you, they do react nicely if you are alongside though, it seems 50/50 if I make a lunge up the inside if they then give me room on the exit when they realise I'm there, but it's not perfect, although still up there with the best IMO for AI awareness, it's just that the 'best' is still pretty poor against reality..
What has surprised me is that having started the career again using a pad on FM3, it wasn't long before I was in cars that are sliding all over the place, and need some real finessing and good car control to keep them going forwards, which is totally at odds with people saying that they cars are 'stuck' to the road.. They sure as hell have some high levels of grip in some situations which is very noticeably wrong, but dang!, the Lotus Elise around Amalfi was an experience in car control and a half!