I'm currently using a Pi, and while it is adequate for the types of games I generally play, it's not the best solution.
A little background - I originally intended to make an emulation console out of a Pi, but then I found a better solution (Ouya) so I decided to build a bartop.
I only intended for it to be a short term novelty item, in fact I made it out of an old dresser (yes, it does look really bad).
It was such a success with my family that I decided to build a proper cabinet.
I've been gradually acquiring everything I need for the cabinet (just waiting for some slightly warmer weather) but I'm going to use my current Pi setup for now and upgrade to a PC later.
This is allowing me to spread out the cost of the build, because I don't have to buy everything all in one go.
In short, I probably would not be building a cabinet at all if it wasn't for the Pi, but I don't see it as the best solution.
If you already have a Pi and you can't get a cheap or free PC, by all means use it for now.
I'm still having a blast with my crappy bartop, and a Pi cabinet is certainly better than no cabinet at all.
One thing I do think the Pi will be great for is my future project - a 'barstick'.
I'm going to have a bunch of spare controls, wood, T molding etc left over from my build and the decommissioning of my bartop, so I'm going to build a control panel with a a Pi inside that I can take to parties, barbecues etc.
The size, weight and cooling requirements of a PC would make this a difficult project, but the Pi is going to make it a snap.