The Vita has the bigger streaming services, but the Fire TV does seem to have better support overall. Although, the Fire doesn't seem to have Crunchyroll and the Vita doesn't have Amazon Instant Video (according to Playstation.com).
Something that some people seem to be forgetting is that the most important part of a streaming device is content. The Fire TV is new, so it doesn't have all of the services that I use. They really don't need to be all that robust on a technical level, which is why the Apple TV hasn't had a real technical upgrade since 2012 (the 2013 revision just made it more difficult to hack). You also don't need to have a large hard drive since content is all streamed to the device.
I'm sure that the Fire TV will get more services as it gets more popular especially now that it is out. Right now the big ones it is missing that I see are HBO Go, WWE Network, Crunchyroll, The Blaze, MLB.tv, NHL, NFL and VUDU. As of right now, it cannot replace my ROKU 2 XD due to the services it is missing.