I've tried both, and while they have their good points, neither really seems to have the "magic" that all those nice little SLRs from that earlier era did (Pentax ME[-super], Oly OM-1/2, etc).
* The Fuji X-pro 1 is big (though light), and seemed to me to have rather clunky handling, with poor viewfinder integration (although the X-pro 1 can display an electronic overlay in the VF, it seemed more confusing that useful; this, at least, might be solvable with software changes). It is also very expensive.
* The Olympus OM-D has a nice small body and classic shape, but it feels kind of cheaply built, and it has one of the worst electronic viewfinders I've ever used: very low res, and very flickery. [I find the horrible viewfinder on the OM-D particularly depressing because the market has recently seen a number of cameras released with vastly better electronic VFs, e.g. the Sony NEX-7 and Alpha A77, and the Nikon V1. Clearly there's no technical problem with making a good EVF these days.]
The appeal of those classic little SLRs was that they were small, light, and quite simple/straightforward to use, but also highly capable and very high quality (and ... beautiful). They omitted gee-gaws without skimping on essential features. In particular, their viewfinders were an absolute joy, huge and bright, with minimal, but useful, information displayed.
Current trends, at least, suggest that camera makers are finally realizing that viewfinder-less models aren't enough...
> "Clearly there's no technical problem with making a good EVF these days."
Sadly, Sony owns a number of OLED patents that prevents anyone from getting anywhere close to the NEX-7's EVF performance. Personally I don't find the OM-D's EVF to be that bad at all, but you're right, it's definitely not the NEX-7.
The problem here is that the classic little SLRs existed because there wasn't anything "better" for the professional shooters. Manual mode was all you got, and the nature of film meant that you didn't need a bajillion menu items just to get a picture out of the camera - white balance, resolution, file formats, etc etc.
I suspect there is no longer a market for a such a thing. The professional/high end of the market demands whiz-bang kitchen-sink featuresets (to be fair, they actually use them), while the consumer/low end of the market demands a whole other set of whiz-bang kitchen-sink featuresets (face detection, a bajillion filter modes, etc).
The market for "barebones camera that does precisely and the basics and only the basics" is vanishingly small. The X-Pro 1 was engineered pretty much for this market, but it has, as you pointed out, so many concessions on the concept that it's not very compelling.
Honestly, your best bet for that is still the Leica M9.
