Would video look better on a projector than on a large computer monitor?

I'm a 14 year old wannabe filmmaker, and the camera I'm currently filming with shoots at 720p as opposed to 1080p. I want to make a feature with this camera (Nikon D5000) but am afraid about how it might look, should it ever be blown up to a 20 foot cinema screen (or possibly even larger), as while it looks fine on my laptop and my TV, displaying it on any computer monitor with a resolution larger than 720p makes it look terrible. My hope is that monitors and projectors display video in different ways, as there's a resolution the computer has to abide by, and with a projector you're just blowing up tiny images with glass and a light-bulb? Am I right in thinking this way? Really could use all the information you can give me…

It would look better on the projector.