I play both, and both have pros and cons. A Caro-Kann player would tell you the French has a problem with the c8 bishop and it's true, but the Caro-Kann also has a problem with the b8 knight. The French is double edged and very sharp and the Caro-Kann is calmer and more solid. It all comes down to the way you wanna play. If you don't wanna lose, use the Caro-Kann. If you want to play for a win since the beginning, play the French.
In terms of theory, I'd say the French is way heavier than the Caro-Kann, more lines to learn. My advice is learn both because you'd be fully covered vs 1.e4 and will have two styles of playing. Let me know if you need more advice.
Good luck.
EDIT: To answer your final questions, which one is better? Both are good. Which one is easier to play and better for beginners? The Caro-Kann. Which one puts more pressure on White? The French.
Which is better? Which has less theory? Which has better win rates?
I already know that the french is more aggressive, the caro is a bit more passive, the french does not lose a tempo, etc.
All I want to know is which is better for black in general, which is better for beginners, which is easier to play, and which one puts pressure on white.
Thanks