I dislike playing against the French more, but oddly enough, if I had to choose which I'd play as black, I'd pick the Caro.
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Just as an aside, I suspect that the French may be objectively worse than the Caro-Kann. In top-flight games, White often gets a nasty attack without too much effort.
It shouldn't make an iota of difference below ~2500 strength, but at the very highest levels and in correspondence, the French is looking a bit creaky.