There's probably two elements to my reply, one of which is down to my own prejudices...
1) The League Cup final is a one-off game, whereas the CL 1/4 final is two legs. So obviously one is a must win, and the other is not. So yes I'd rather win the League Cup final on that basis. This would be my logical answer to your question, irrespective of how important I think each competition is;
2) In common with
@robinamicrowave above, of the four trophies available, the CL is the least important to me.
I'd rather win the FA Cup than the CL, and I'd rather win the League Cup than the CL. So yes, I'd have preferred to win the League Cup final, but I realise that this element to my reply is more controversial and based on my own issues with the CL!