That's an oldschool preview system

Composite video sends a 720x480 interlaced signal which gets unstretched to a 720x540 interlaced image, and you're feeding it 1280x720 image. The image is first reduced in size, then squashed then unsquashed, all-the-while trying to convert from progressive to fields. (google "interlacing" for more info on that). So, basically your signal path is going to BY IT'S VERY NATURE tear your image to shreds... and all of this is assuming you're in NTSC format. If you're converting from PAL to NTSC or reverse, visual artifacting gets compounded :<

If you need to preview it full screen, and you don't have access to a second monitor, I'd opt for a RAM preview in After Effects. If you need to view it on a TV (if for instance the final product will most likely be viewed on a tv) then make sure your AE sequence settings are set to NTSC (or PAL if you're from Europe or other PAL-broadcast country) DV.

Good luck. You're gonna need it. I remember going CRAZY when I started learning video stuff trying to figure all the above out. It's a nightmare