If the aspect ratio is the same, I don't know why 1080 content on a 720 display would have black bars vs. the same content in 720 on that 720 display.
If you take 1080p content at a ratio of 16:9 and put it on a 720p screen, the content will look stretched and the black bars are much more pronounced. Only 720p content looks native on a 720p screen. The way around this is to be able to change the aspect ratio to "wide" ...most TV's do this natively. However, there are apps that will make the content scale to correct ratio automatically (or if the content is natively scaleable) from 1080 to 720 and vice-versa.
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