A full HD LED TV is 1080p. Your GX660 is an awesome notebook and the HD5870M will be able to handle most games at 1080p if AMD worked with the developer. Games like Witcher 2 at initial release not so, but after patches and what not should be fine.
Also you can use lower resolution on HD TVs. The TVs are huge. If you are planning to play games on a TV 2 ft away, 720p may not look great, but you'd also be stupid. You should be 10 ft away from the TV and at that distance, 720p, the HD5870M will be able to play games at very high or ultra settings and you should see something amazing.
If you read on other forums, players who use large HDTVs can confirm, 720p at a safe distance away looks as good if not better than 1080p on your laptop screen at 1080p 2 ft away from your face.
So for your laptop, I'd play @ 1080p at whatever setting you can get, medium/high. If you play on your TV, downscale it to 720p and crank up the settings, very high/ultra with 2-4X AA. You won't need 1080p when you are a safe distance from the HDTV, so it's better to get the eye candy extras like SSAO, Depth of Field, Motion Blur etc which you couldn't use at 1080p with high res textures. 720p with eye candy extras will look much better on your HDTV than 1080p with medium settings without the eye candy extras.