Lots of answers here, some of them from people who have not handled one or the other of the cameras.
The short answer, if you don't want to read any further, is they both are good choices.
I have had several M43 cameras. Currently I have the GH2, which is the top of the Panasonic line at the moment. I wanted a more pocketable M43 too, so I looked at the EPM1 and the GF3.
Similarities:
Both the EPM1 and the GF3 use the same sensor. Both of them do considerably better than the earlier generations of this sensor in terms of sensor noise and higher ISO performance. You can do quite well in terms of image quality with either of these cameras.
Overall performance in terms of focusing speed and responsiveness is very good; I would, however, give the edge to the GF3 in lower light situations (small difference, but it is there).
Both cameras can be used in fully automatic, scene modes, or manual or partially manual modes (aperture or shutter priority).
Controls on both, while minimal, are very similar. The GF3 allows some programmability of buttons, not sure about the EPM1 (I assume it does also).
Both produce very good picture output (yes, even the jpgs in the GF3 are quite good). Olympus has legendary jpg photo color balance, but I find the GF3 to produce some of the very best looking Panasonic jpg output ever.
Both are small enough to carry easily.
Both are excellent cameras.
Differences:
The EPM1 has a hotshoe, which means it can use an external viewfinder or a regular sized external flash. The GF3 does not. However, the GF3 does have a built-in flash, which can be popped up when needed. The EPM1 comes with a tiny external flash that you must attach to have that capability.
The LCD in both is 3". However, because of the way Olympus chose to use the display ratios, actual visual area is much smaller than that of the GF3. (Try them out in the store next to each other, you will see what I mean). The GF3 has a nice, bright display which is very easy to see outdoors; Olympus has been a bit behind the curve on this in the past, however with the external viewfinder attachment, you would have an advantage over any LCD only camera.
The user interface in both cameras is pretty good. I personally prefer the Panasonic as it seems more intuitive to me, but that is one of those things you will have to try out yourself to see what fits you best.
Image stabilization: Both camera systems use IS. Panasonic applies it in-lens, Oly applies it in-body. Advantages for in-body (IBIS) are that it can keep lens size down and you can use any lens on an IS camera body, (even a vintage one attached to camera with an adapter), and get image stabilization applied. However, the general consensus is that IBIS is a little bit less effective than OIS (in-lens stabilization). Both systems do work, though, and both are effective at reducing camera shake blur in lower light situations (within limits, of course).
EPM1 is a bit slipperier to hold since they did not put any kind of molded grip on the metal cased front. The GF3 has more places to rest your fingers and grab the camera.
SO, what should you choose?
Go to a store that has both of them, pick them each up and play with them (if you are in the US, Best Buy actually stocks and has both of these cameras on display). Pick the one that feels best in your hand and that has the control layout that makes sense to you.
For me that was the GF3. I fell in love with the little thing the first time I played with it and finally caved and bought one over the holidays. I am having a blast with it.
For others, the EPM1 had the same effect, and they too are enjoying the heck out of it.
You really can't go wrong with either.
Good luck!
-J
