I am afraid I have not been able to interpret the title of this thread, so I just think that the never-ending debate, which I have kind of expected to reappear, is starting again.
When I played the Caro, most of the time I had to combate in the Exchange (!) Variation.

(2000~2200 players) That was good. But what I dont't like about the whole defence is just the Classical Main Line, when Black has to take on e4, then wait again patiently for whatever minor piece-configuration White wants to try. Yes, it's solid, yet I don't have a feel for it.
When I play the French the occurrence of exchange variations decreases, and I meet a wider variety of white tries and usually have to know more theory, but I like that Black gets more opportunities to choose the direction of play. (And those ..e6+..d5 pawns usually remain, which gives the whole defence "a feeling of home.")
If you can build the rest of your Black repertoire around your choice against 1.e4, be it 1..c6 or 1..e6, then you r less likely to shift later.