After trying to watch a Vimeo video on my Panasonic TV, I'm now sold on the Chomecast:
1) pressing buttons on the normal TV remote sometimes didn't work. Batteries dying? Not clear. True a smartphone's batteries only last a day, but when the power is dead, it's obvious.
2) using up/down/left/right keys on a TV remote to gradually pick out letters on a search box is not fun.
3) after this process, the Vimeo TV app gave me 9/533 matches, but none of the matches were my video, nor was there a way to see page two of results!
Here's the eventual workflow for watching Vimeo on the TV:
0) associate TV Vimeo app with my Vimeo account
1) boot up laptop, log into Vimeo
2) laptop: find video, click "Watch Later"
3) TV: wait
4) TV: magic happens, video appears on the beginning of the Watch Later list
5) TV: click Select to watch first video
After all that, the video play was like a laptop: audio/video occasionally stutters. Pressing play and waiting a minute seems to help, but it's not clear. On the other hand, video and audio quality is quite good.
It looks like the Chromecast version of this is:
1) use tablet to find video
2) click "Send to Chomecast"
3) there is no #3
(And yes I know Vimeo doesn't support the Chromecast; I'm just going over the overall thing here.)