720p and 1080i has a lot of difference. Interlaced video, the "i" in 1080i isn't quite as good as 720p. Benjamin Higginbotham, the Technology Evangelist, explains why in the above video why you should stop using 1080i.
When watching interlaced videos, you're really only seeing half the resolution because the image is split into two filed that alternate very quickly. This tricks our eyes into seeing the full image even when it's not being displayed at the same time.
720p gives us 720 lines of horizontal resolution in each frame, and in 1080i, you only get half of 1080 lines of resolution in each frame. It's not that big a deal, since if you're not used to it, it's hard to even tell the difference. But objects in fast motion will look like they're smearing across the screen instead of being natural.
While 1080p is definitely your best bet in terms of highest resolution, don't think that 1080i is just as ideal because the number's the same.