As far as I know, the core of Xenko and most of it's component aside of the editor are open-source. So you can basically take a look really easily at how they implemented Physics to "mimic" it to implement the parts, bits and pieces that you may be missing.
I know, with experience, that, for example, there is no joint component by default in Xenko, you have to write you own physics joints, for now at least.
If you're looking for a car example, the best I could give you so far is a link to a thread I made when I decided to write my own physics joint constraint script. (it also has some of the code I use there)
It's not perfect, but it uses physics completely (including in the double wishbone suspension):
6DOF constraint script code
Car example with full physics + sort of how to setup
I don't know if bullet's car-related classes will ever be implemented in the engine, but as soon as they get the time to give physics some love. I guess so.
Hm. I never really compared physics to bullet, so I could not tell you, sorry! I'm sure that some people benchmarked it though!
Also, don't forget that initially, bullet is a c++ library that got a C# wrapper (BulletSharp If I can remember) and then is use by Xenko as a dependency and declares it's own classes dependant on those.