Fujifilm X-E1 or Olympus OM-D E-M5?

I own both, so hopefully I can be helpful.

Tons.

Hands down Fuji, but i say that from an OOC jpeg standpoint since that is what I use it for. When raw support becomes available from Apple, I'll know more on that. Don't get me wrong, the EM5 is great, but the APCS XTRANS takes this category, hands down.

EM5 utterly destroys the Fuji for now in this category, and has more lenses coming soon. Right now, Fuji has no native ultra wide and no long telephoto. People might argue that those are not areas a rangefinder is really meant to cover, but this isn't a rangefinder and for practical purposes, is a bit crippled until lenses like the 10-24 and the 55-200 come out, as well as the 23mm (if you like 35mm FOV) and the 56mm (if you want a fast portrait lens that isn't so slow focussing due to being a macro lens.

EM5, on the other hand has you covered (FF Equiv) from 14 - 600mm.

There are some great quality lenses for the EM5 if you want to spend the money. I like the Panny 7-14, Oly 12, Panny 25, Oly 45, Oly 75... But I only own the 7-14, 45, and 75, and would get the new 17 when it comes out soon if I didn't think I was going to ultimately phase the system out in favor of the Fuji. When the rest of the X lenses on the roadmap are out, I will stop using the M43 system. If not though, I would have ended up with the 7-14, New 17, New 42.5mm, and the 75, and would be more than happy with the build quality, despite the non mechanical manual focus that I dislike on both systems.

Fuji lenses? As good as some of those M43 lenses are in build quality, and they can be GOOD, Fuji really makes an uncompromising product in my opinion. It just feels expensive. Fuji wins here so far, but they are light on lenses, so it may not be a fair comparison yet. I don't suspect, however, that they will decrease build quality as they go.

Features goes to the EM5, although one of the things I love about the Fuji is it's ability to let you get out of your own way and play as little as possible with menus and other garbage that many photographers find useless. This really depends on the person, but the one area where the EM5 really kicks the Fuji's butt is with the FP flash mode. This may not be a big deal to many, but it is painful for me. Until Fuji builds a flash that will do this, I will always think twice about phasing out the EM5/M43 system.

Sure, I like them a lot actually, but did you have any specific questions about them? I really like that you can just shoot raw and process different simulations in the camera to see what suits you best.

Any time!

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A lie gets halfway around the world before the truth has a chance to get its pants on. - Sir Winston Churchill