with a game console or BR player, you normally wouldn't see a big difference in image quality outputting 1080p from a tv with 1366x768 native res, assuming you sit back the usual tv viewing distance away. with a PC however, it's a different story. your mileage may vary, but personally, having tried it, text were hard to decipher and image quality wasn't all that impressive over native. it doesn't hurt for you to give it a try though, and decide yourself.
performance-wise, i'd reckoned there'll be a drop in fps, though i'm not sure. however, with the added software running on the TV to downscale the 1080p image, you'll be seeing some input lag, that i am sure. how much lag you'll see depends on the TV.
my advice from experience; stick with native.