Just to get things out of the way, I'm new here and not really sure where this would go. It deals with graphics/resolution, so this looked like the best place. If not, relocate it to a more suitable location. Also, if this has been answered elsewhere, feel free to post the link.
Anyway, I have a question that I can't seem to find an answer to anywhere, even on other sites. I have an LCD TV that has a native resolution of 1366 x 768 and can accept 1080p and downscale it. My PC is connected to it via HDMI and I have defaulted it to display at the native resolution. However, I've been wondering, when playing games such as Crysis and such, should I output the game in 1080p or the native resolution? I understand 1080p will make it run harder, and it will downscale anyway, but are there any upsides? For the record, my TV is a Toshiba 32" 32C100U1. I don't know the quality of the scaling software compared to other TVs, but it seems pretty good. Also, my GPU is a GTX 560 Ti 2GB, if it matters.
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.
I'm not sure why you would be running at 1080p unless compatibility is an issue. As to upsides for running at your display's native resolution: obviously no conversion happening, and primarily your graphics card isn't going to be rendering the extra wasted pixels (around 51% workload compared to that of rendering 1080p resolution). You already have a fairly stout video card, so either way, you should be able to crank most settings to max at least with a majority of games on your native resolution and that card.