1080p = 1920x1080
Depending on the monitor, a standard res is 1920x1200 but it could be higher.
Edit:
22" and lower (widescreen) will get you no higher than 1680x1050 that I've seen.
24"+ you will most likely get 1920x1200. Dell offers a 30" beast that is like 2500x1600.
Refresh rates on monitors are more adaptable too, so you have more to choose from. Usually a little higher too.
Most TV's are 60hz, newer tv's have come out though that do 120hz which is higher than my monitor at least.
Edit edit:
120hz is a direct multiple for 24 frames which causes movie sources to be more fluid.
In general, I'd expect a better picture off a computer monitor, but then we are still getting into brands, size and resolution.