I haven't owned the EPM-2, but I routinely use the EPL5 which I bought as a gift for my mom. I got the GM1 for myself.
For me, the big advantage of the GM1 is how silent it is (regardless of whether you're using the e-shutter or not). The EPL5 has a discreet but very audible (and I might add, pretty sexy) snapping sound when you take a picture. The GM1 is almost noiseless. Also, it goes to T/16,000 for shooting in broad light and suffers no shutter shock. With the Oly bodies before the EP5, you have to be careful to avoid that.
Oh, and the main reason I bought it was because of the fantastic kit lens. It's a step up from my 14mm prime, with more contrast, wider angle an and OIS.
But you do get the hotshoe, a somewhat better grip, IBIS, longer battery life, and these days also a killer price for the EPM2. I thought I would care about the Wifi but I don't use it at all.
I like the GM1 a lot better. I bought it because I also wanted to 12-32mm lens.
The near mechanical silent shutter is wonderful. I don't use silent mode since the mechanical shutter is so quite already. I don't shoot faster than 1/500 indoors, but I've gotten banding under fluorescent indoors when I forgot to adjust my ISO.
The LCD is much nicer and I feel the screen is more sensitive to touch. I think the LCD is much nicer under bright light as well but I haven't compared them side by side.
The GM1 also focuses much faster with the 20mm, which is my preferred lens on the GM1.
I've only used the wifi function a few times as a remote release.
Unfortunately the GM1 doesn't have the option to use auto ISO in manual mode or the ability to set a minimum shutter speed.
I didn't find IBIS very useful in the e-pm2 so I didn't miss it with the GM1.
As small as the EPM2 is, the GM1 is surprisingly smaller. Wifi functions are pretty great, too, and if you do a lot of video the GM1 has much better video recording options. And as others have said, the GM1 is essentially silent, even with the mechanical shutter. Both a positive and a negative, if you like a shutter sound. (GM1 lets you use a fake shutter sound, which sounds pretty gross.)
IQ-wise, there's not much between them. I tend to prefer Olympus colors, but both sensors are modern.