"Arcade Only" cars are all stock... they are the "Recommended" cars used in online spec races I believe.
"Favorites" are just that - your list of favorite cars from GT Life, with any modifications you have made to them preserved.
All of the opponents in Arcade Mode are stock, chosen based on a combination of your car's PP level and tires. Street cars get street cars for opponents, race cars get race cars(not necessarily of the same type). You can fine-tune the difficulty by entering with a power-boosted car and then removing the upgrades or adding ballast/limiter to a stock car or by changing to lower-grip tires after loading the race(or going in the other direction to make it easier of course).
Most people seem to report having a hard time getting good fields or competitive races when using cars that they have tuned, although I don't know for sure whether this is down to using cars that are very high PP(there aren't very many high PP road cars for it to choose as opponents) or whether something just gets messed up whenever you use an upgraded car. I most always run stock in Arcade so have never studied that.
Technically, it probably isn't PP that determines your opponents since PP wasn't around when the game was first released. It's probably power and weight... other installed parts don't seem to have any effect.
