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Adam, I can only offer an anecdotal perspective based on the reviews I've followed by others immersed in m43. My impression is that there is some really nice glass from Olympus and Panasonic, and that certain of the Panasonic Leica lenses, such as the 25/1.4 and the recent Nocticron, share some Summilux-M rendering characteristics.
I've contemplated the merits of adding a m43 system... but currently don't see how it will give me anything more than what I get with my current gear, other than more money in my wallet. Mind you, I'm shooting with a Canon 1DX and Leica M. The Canon gives me top of the line AF for sports/action, which I believe is still a shortcoming of mirrorless, despite manufacturer marketing claims to the contrary... Maybe the performance is getting closer, but there is still something lacking, IMO, when it comes to high speed, erratic subject tracking, as well as decent telephoto options. On the other hand, Leica M offers me amazing glass in a very compact form. And both of my kits facilitate the 'full frame look' when I want it. Size-wise, some of the better performing m43 cameras aren't all that much smaller than mainstream DSLRs. Add an f/0.95 m43 prime in order to get the look of an f/2 lens on full frame, and those lenses aren't exactly small. In fact, probably larger than an M with 50/2. I too have been curious about the GH4 and if I was to get into m43, was leaning towards the GX7... but looking at it on the camera size website, it's very similar to a Leica M and the lenses aren't any smaller. It leaves me wondering why I'm even considering this...
What has probably held me back the most is small sensor image quality. I think it's generally fine, especially at lower ISOs. But from the full-rez files I've looked at, they've reminded me too much of file quality I got from my LX3 P&S camera's RAW files, or those from the 1" sensor in the Sony RX10 I demoed for about a month earlier this year. It's something about the noise/grain structure that starts to feel coarse and fragile - something I don't see with APS-C, APS-H or full frame. That said, I've seen some nice ~20" prints from m43 by a master printer that were indistinguishable from other formats in a portfolio that included FF and Pentax 645D... though the m43 images were shot with a telephoto and weren't of extremely detailed subject matter, such as a forest landscape scene.
If I was getting into photography now, without any prior experience, I would probably be tempted by m43 due to the cost of entry and the relatively extensive system options compared to some APS-C mirrorless options. And I believe your friend has reason to be excited about some of the Panasonic Leica lenses. As someone immersed and invested in Leica M, however, I don't believe m43 offers anything more in terms of that difficult to describe organic lens rendering quality we all seem like so much about Leica M with M, ZM, CV lenses, etc.