Well, I don't have a 'favourite' undurance car yet. I don't think you can actually have 1 favourite car, simply because you don't use the uber-cars in every single endurance race.
It's a shame people use F1 cars or Le Mans cars in endurance races like the Nurburgring 4 and 24 hours. In my eyes that's just lack of skill, do you really feel better when you win with 20 laps more than the opponents? It's not going faster in B-spec if you use a faster car. It's just like having aimbot/wallhack and stuff like that in Counterstrike or a similar game. You have a secure win, you already know that you can't lose unless you're a very bad driver.
Anyway, It's a 'different' story when you use overkill cars in races like the Suzuka 1000km race. I still don't agree with using a car like that just like the xx hour endurance races, since the opposition is using JGTC cars, but using overkill cars in races like that is not always lack of skill, people can be unpatient as well.
Anyway, I haven't done any of the endurance races yet, but if I start with it I'll always look for the 'perfect' cars, in other words cars in which you can win with the smallest gap. I would have a great day when I do the Nurburgring 24 hour race and in the end I win with less than a minute in front of the other car. Example of such a race: In Gran Turismo 3 I did the Rome endurance race with the Spoon Civic and in the end I won it with less than 30 seconds in front of the much faster TVR Griffith. THAT is a real race, I had to push every single second of the race.
Used the Toyota 7 there both times! 
