Your TV has (at best) 1920 x 1080 pixels, possibly less if it's 7 years old. That has nothing to do with the size. This is far below the resolution of the 7D - to be precise, it's approaching 1/3 the resolution or 1/10 the number of pixels.
But wait, there may be more. If the PS3 is feeding the TV a standard 1080i30, 1080i25 or 1080p24 signal, that uses "chroma subsampling", so that although the luminance is at 1920 x 1080, the colour information is not. Many TVs provide a "monitor HDMI" input that avoids this, but I don't know what your PS3 and/or TV does and how you've set it up.
The TV may *look* sharp because it's doing what's known in the video world as edge enhancement, which is what stills photographers call USM sharpening. This would be why you perceive the TV as "sharper" - a more trained eye might think the opposite.
In summary, displaying the images on a TV is one of the worst possible ways to evaluate their sharpness. Most of the difference is far above TV resolution, and what it can see the TV may be trying to equalise.
EDIT - I am assuming in the above that the PS3 doesn't have a way to "zoom" in to look at the actual pixels (you would be looking at 1/10 of the picture and have to scroll around), but instead just shows the entire picture fitted on to the screen (pillarboxed).