Right now, currently speaking, not having a Roku to try, I would say that CURRENTLY the FireTV is the fastest of all. there’s no real wait on anything. It’s so fast for me it’s really hard to imagine anything being faster. Click FF and it’s ahead by 30 seconds and playing again before you can click a second time. Click something to play and it’s there. but then it’s DIRECT to the Tablo itself, only 1 jump, FTV to router, router to Tablo, nothing else in between and if the Tablo is wired to the network, so much the better. You are going directly with nothing between, and the memory and processing power and network reliability of the FTV is currently the best, If Roku comes up with a 4 soon, it could get interesting.
Otherwise, I’d say it’s a matter of preference, what you plan on doing with it, what else do you want, need or prefer, how much money do you want to spend, etc.
Although big Amazon customers, I bought the FireTV stick on the thought of using it as my Tablo interface and nothing more. In that respect, it’s not much more expensive than a very good quality HDMI cable, is it? So it’s sort of like buying Tablo, then buying a high-end cable to connect it to the TV (which you can’t do, of course!), but you have the FTV device instead of a cable, it’s that quick and simple.
I will say that the latest firmware upgrade to Tablo has made my Chromecast experience a lot better, too! It’s also quicker and more stable than it ever was, but maybe my Tablo had an issue with the prior release. this one fixed a couple of major things for me and Chrome/Chromecast. That method will always be slower as you are doubling things up across the network, stream to PC, then cast to Chromecast. This method relies on a better, more stable network than other methods might.
Figure out what you want out of your Tablo, your current future use of the TV in general, what do you want to get out of it, other aspects of your viewing habits, do you plan on using other Internet-based channels, etc. and decide from there. I can see pros and cons to each, but pure speed requires a direct shot from the Tablo to device to TV. The shorter more direct shot, the better off you may be.