Maybe that wasn't a good translation. I recall Bareev visiting my club here in Southern California, and in a lecture described the French as not quite correct, or something like that. I think he said "not correct" but I know what he meant. Still, it's more imbalancing than the Caro. 

If given a choice, I'd stick to the Caro-Kann. I prefer reliability (and Vajajay).

I'd chose the french, it is more clear than the caro, there is somehow always a clear way to equality, there are not many ways for white to get a kingside attack, and it is much easier to equalize for black than in other defences, tbh I think every french player would lose 200 ratingpoints if he'd play any other defence, they reach only their strength because of this defence.
But I'd play the french only as 2nd defence because of the exchange.
Also I do not like the mainline in the caro where white castles 0-0-0,
I just feel lost there as black. Though I have to admit I never played any of these defences otb, I only have some blitz experience (especially in the french).

The cool thing in the french is I only think about equalizing and I am satisfied with that, in the sicilian or the modern defence I am not satisfied reaching equality, I always think about winning.

Let´s say that someones ask you to choose a vegetable to eat for the rest of your life for you. He is going to buy the vegetable, wash it, cook your diner every day but you only can choose cauliflower OR spinach. What would you choose and why?

Both are totally suitable for your aim. You can check games by the late Karen Asrian for "fighting CK" at top GM level (+ Anand, Ermolinsky...), and similarly Cheparinov, Morozevich (+ countless others) for the French. It was even commonplace in Russia to play the French until you reach a decent level (~2400) and then start looking at the sicilian, this may help you for your plans. But if you have any ambitions, you should forget about "style" and "reputations", and take on concrete variations by the horns. In this respect, CK feels easier to discover by yourself, like Korchnoi with the English. The less you read in a book, the more you find on the board!  
More importantly : to reach 2400+ you have to be a fighter, no matter the openings.

Let´s say that someones ask you to choose a defensive system for the rest of your life for you to reach 2500. He is going to buy books, cd, pay your tournaments but you only can choose French OR Caro. What would you choose and why?