When comparing Panasonic GX1 vs Olympus EP3 one must keep in mind the fact that whereas the GX1 is meant for those who want a DSLR type camera without actually buying a DSLR and the EP3 is meant for those who have the abilities to shoot professional shots without the help of a DSLR.

The Panasonic GX1 is meant for those who want to make the transition to a DSLR but not want the size and bulk. On the other hand, the Olympus EP3 is specially designed for advanced users who know the nuances of photography. In other words the GX1 is very much for the crossover crowd whereas the EP3 is for those who have already made it.
Features: GX1 vs EP3
The Panasonic GX1 is robust and built to last. You can lug it around anywhere and everywhere and in particular, wildlife photography and wilderness shoots are its specialty. The Olympus EP3 is also sturdy but has very nice color rendering that is loved by many Olympus fans.
For both the GX1 and the EP3, capturing still life and motion is easy and this adds to the lure of both the models. The differentiating factor would be the easy adaptability that is provided by the GX1 with its flexible controls and settings.
Performance: GX1 vs EP3
As mentioned above, both cameras deliver outstanding results like a DSLR in terms of image quality. Many photographers are concerned about the autofocus speed which has been improve in both GX1 and EP3. Based on the specifications, the GX1 does seem to have an edge over EP3 in terms of AF speed. However, under normal use, you proabably won’t feel the millisecond difference between the 2 cameras.
Panasonic GX1 AF Speed
Another point of comparison will be the image quality at high ISO. According to stevehuffphoto.com ISO test, the GX1 offered better picture quality than the EP3 at ISO 6400.

Handling: GX1 vs EP3
The GX1 is both sturdy and adaptable to conditions whereas the EP3 might need some protection in outdoor photography. However, the EP3 has an additional dial which makes it quicker when changing setting. I find it easier to grip the GX1 than the EP3, however, if you have bigger hands and prefer the Olympus then you can remove the standard grip and replace wth the larger grip, MCG-2.

Price: GX1 vs EP3
The best things in the world come at a price – both the Panasonic GX1 and Olympus EP3 come at a hefty tag depending on the specifics of the model and the additional add-ons that you want. The GX1 with the 14-42mm kit lens is priced at $779 versus EP2 with the 14-42mm II R kit lens at $899. However, if you wanted the X VARIO PZ 14-42mm/f3.5-5.6 powered zoom lens to go with the GX1 then it’ll cost you $949 which is a lot more costly than the Olympus EP3.
You may be interested to read our price comparison review on:
Olympus EP3 vs Panasonic GX1 vs Sony NEX-5N Price
Panasonic GX1 or Olympus EP3 Overall Thoughts
If you would ask me which one of the GX1 vs EP3 would I choose; my biased opinion will be the Panasonic GX1 despite its higher price and not so favorable color rendering. I prefer the GX1 because of the faster, reliable autofocusing and the slightly better image quality in low-light condition as I find myself doing more natural light photography with lenses faster than f/2.8.

I’ve not really seen or felt the difference between the GX1 and EP3 you describe here. The GX1 is not a DSLR-like camera and the two cameras are very similar in handling. I’d rather say that both cameras are popular among those shooting with a DSLR but want a smaller system camera for occasions were size matters. Personally I’ve favored Panasonic and owned the GF1, GF3 and currently own the GX1.