If you resize in a shitty manner, then both will look less than great. Here is a very good way to tell: don't resize the display image. Now notice one playing at 720x480, the other at 1280x720. Which is obviously better? Then for 1080p stuff (of which there is some, mostly movie rips now), the resolution more than twice that of DVD. If you can't see the difference, you are blind, there is no investigation involved.
My monitor is 1680x1050, and I have no problems with anything. I doubt your computer is really ready to handle that resolution for anything but a desktop view to begin with. Yes, resizing takes more power.