I find them to be quite unpredictable, although they do have strong tendencies for certain issues on certain tracks. Sometimes they don't hit you very much as long as you're aware of how they drive and you can almost treat them with respect with lots of good battles, other times they act like it's their first time playing a racing game besides Burnout and your best option is get past by any means necessary and get away from them ASAP. I've never noticed anything that suggests they drive any differently whether damage is on or off, though.
I've mentioned it before, but if they even have a hint of a look at Algarve T1 just let them go ahead or you will die -- if you can convince them to cut the corner you can often get back past in the aftermath, otherwise you can often re-take the spot in the hairpin. They were quite swervy at Bannochbrae which made side-by-side very risky, but they were rather slow overall. I'm currently working on a career race in Super Trofeo at Road America and they are just plain evil there all around the track, diving super late into every corner, turning right down to the apex as if you aren't even there, and of course their known impossibly consistent flat-out runs through the Kink. Close racing at that track seems to not be wise. But at other tracks they aren't nearly as aggressive.
It seems like there's usually at least one place per track where you have to watch out for being run over, and another where they will back off way too much. Some tracks have too many of one or the other which can cause problems. It takes a lot of track-specific learning to work with them. I still think they just aren't very good at seeing you because when they do they're pretty good at staying close with minimal contact.
When they hit the brakes from what I can see between watching Bob and the other bots they very slowly and steadily apply pressure from zero up to whatever the max is. That means they always start braking very early, but don't really start braking hard until a second or so after they hit the brakes. This can cause a lot of that brake-checking - as well as the odd back-and-forth where you pass them when they first brake but they can continue to brake super-hard late into the corners and pass you back.
The other overall annoyance I have is that they drive completely differently when they are behind you than in front... braking much later and trying all kinds of different lines through the corners, some of which are really poor ideas. They're much better behaved around each other, taking looks and sometimes backing out too easily but not trying anything suicidal as a rule. It just seems to be proximity to the player's rear bumper that causes them to go insane... not a particularly great design.