The way it works now on the 360 is if you have a game like Fable or Jade Empire which by default is made for 480p sets, if the console it set to a resolution of 720p, the image will be squished down and you will see black bars around the screen. Games like these cannot be upscaled because the textures would come out too pixelated. The solution is to set the console resolution to 480p while you're playing these games. Newer games like GTA: SA for the Xbox are automatically upscaled to 720p to fit your TV's resolution.

Now I don't know exactly what the resolution guidelines for the PS2 are, but that might just be the case when playing PS2 games in 720p/1080i/p