Since you are looking at both the GX-1 and EP-3, then this 3 parts write up comparing the 2 will be rather useful:
Panasonic GX1 vs Olympus E-P3
ISO wise, the GX-1 is better, out of camera Jpegs, the EP-3 is very good.
I usually takes 100s of pictures on my walkabouts, and will not have time to pp them, hence the EP-3 is the camera for me.
I am using an EPL-3 right now, the lite version of the EP-3, with equivalent performance, but smaller and cheaper, and have a add-on handgrip.
With a pancake lense mounted, it is really small, which is what i like about the M4/3 system. However, as you mentioned, you have big hands.
My advise for you if you have already choosen the M4/3 system is: look for a lenses first, then the camera. Those m4/3 lenses retain their value well, especially if you have choosen the holy trinity of M4/3 lenses. There are actually 2 sets of Holy trinity lenses for m4/3 right now, one set for the budget conscious, and the other for the richer. This is where the M4/3 has a edge over other mirrorless system right now. Mature system with many good lenses selections.
In his blog, Tyson Robichaud described 2 sets of Holy Trinity lenses for M4/3, for set for the budget conscious, and another set for the money is no issue.
It’s not the size of the boat, it’s the motion in the ocean.
Holy trinity for budget conscious:
Panasonic 14mm f/2.5
Panasonic 20mm f/1.7
Olympus 45mm f/1.8
Holy trinity for the money is no issue:
Olympus 12mm f/2.0
Panaleica 25mm f/1.4
Panaleica 45mm f/2.8 OIS Macro