Is there any advantage with one over the other? The firetv is $79 now, so I'm leaning towards it, but I'd love to hear your insight as I'll be new to the XBMC world.
Sure, I would be happy to lend my insight between the two.
The FireTV is an ARM box deep down, which means its CPU power is somewhat limited on single core performance (which the XBMC interface loves). This port can't use all XBMC plugins, and the CPU of the FireTV isn't powerful enough to decode what the GPU couldn't decode from the factory in every case. It does a pretty good job for an ARM box- I think it the best one in that category especially for that price. I think the FireTV is a good option for those on a budget, or those who want Netflix/Amazon/Hulu streaming capabilities with XBMC on the same box.
The Chromebox is a full x86 computer. In Openelec mode it runs what is THE most loved (by the developers) port of XBMC that can use almost EVERY plugin ever made. As a bonus, unlike a FireTV, the Chromebox has enough CPU power to decode almost ANY file you throw at it and not just what the GPU can handle. This extra CPU power also means you can use better skins and a bigger library with less lag. It is fanless and small, and it works very well for the job of XBMC.
It comes down to priorities.
Where the FireTV will lag a little on the interface, but maybe not if you use a skin like Bello. It should still play most local content, but not admittedly everything if you have some esoteric library like mine with some large VC1 files. But for that it will give you Android, which means the box can do more easily for more people- like games, Netflix, etc. That makes the FireTV the better all-purpose box. It is pretty amazing for what it is, and beats what $300 could buy me in 2011.
Meanwhile the Chromebox is meant to be a XBMC appliance, that if you know linux can be hacked to do cool stuff, but otherwise is a XBMC appliance. I like that about it personally, I feel simple and appliance like is the best case. So I recommend the Chromebox more for people who want "the best way to stream a mkv.". On an XBMC scale from 1 to 10, the Chromebox is a 9 (only a custom Nvidia rig is better) and the FireTV is like a 7.