Rendering direct to a movie format is never recommended (lots of reasons, one major one being if anything goes wrong, all output is lost and you have to render from the start again, versus just having to pick up rendering where you left off if you are rendering to frames). Compositing the frames into animation in post also lets you control video compression etc better too. Lots of free applications for doing just that, so it needn't cost any money :) I can say from years of rendering animation that there is no benefit, and many drawbacks, to rendering straight to a movie format.
I suspect this is due to the viewer application doing something to the avi - another reason to render to still frames is you can open an individual frame and make sure it is fine. Even if you plan on still rendering to movie format direct, I'd do that just once, even just for a few frames, and make sure your images are coming out correctly. But basically, there is no way I can think of that your 1280x720 render is not still 1280x720, which would mean it is being displayed incorrectly in the viewer (that is, whatever is playing back the animation). You could right click on the avi file and check what dimensions it says it is.
Hope this helps!