IMO you should carry what ever you are the most comfortable and proficient in shooting.
For me, (I have bigger hands as well) I am comfortable and proficient with my full size 1911.
I don't carry on my person often but when I feel the need it's at 3 o clock IWB with an over shirt.
I have a light build (6' 180#) but it really does not show at all. At first I was self conscious because of the weight and all, but that goes away when you realize it really doesn't show.
We have a 938 which would be a great carry gun as I could put it in my pocket and all, but it's just too small. I feel, if I needed it, I would pull it out and drop it like a cell phone. Additionally, although I can aim and shoot it very accurately, I shot a IDPA stage with it once and could not hit a cardboard person to save my ass.