x86 definitely and for various reasons. I think I have to explain my point, because I want to convince as many people as possible:
1. Compatibility.
It's not a secret, x86 has the best compatibility available. OS, software, games and such... nearly everything will be compatible right at the begining, without any work needed. And that's something that ARM lacks. Of course, for some software, some people might be able to do the port job... but what about games ? Of course such handheld would be able to run any Linux distribution, Windows but also Steam OS.
2. It's a niche that has yet to be filled.
Back in the days, Pandora was unique. An open source handheld, with powerfull ARM CPU. Back then, ARM wasn't big, and best ARM CPU available were ARM11... but nowadays ? ARM is big. You can easily find chinese Android handheld for emulation. But there are also powerfull devices such as Nvidia Shield. Sure, none of them are compatible with Linux... but then we're back at the first point: x86 fill this purpose in a better way. Back on point 2, there's no x86 handhelds. None. Sure, there are tablets, but they lack proper controls. With that, you can play any x86 games but also emulators, and that is a HUGE thing.
3. Hardware capabilities.
That's the final point. In theory, ARM Cortex A15 CPU and Baytrail CPU are supposed to be on par in term of horse power... but that Intel HD GPU in Baytrail SoC is really capable. Playing games such as Unreal Engine 3 games, such as Mass Effect 3. Imagine all those games availables ? Indie games, oldies, emulation but also recent games.
And you know what ? Baytrail is already capable of such, but its successor, Cherrytrail (which is supposed ot be released this year) has 4 times the GPU power of Baytrail, and the process node is 14nm, which means nearly the same power consumption.
By going x86, Pyra is filling a niche that is yet to be filled, but also offer more appeal to be something more than niche. Just the fact that it could be considered as a Steam handheld makes it a lot more appealing. I know that some people think that ARM is a better candidate, and I can get their point. But they also need to understand that there's a lot of ARM devices that can fill this job. Heck, Pandora was one. But an x86 handheld ? Pyra might be the only chance to ever get one...