It only makes sense that the HDMI source can send out only ONE type of signal at a time. Since most higher-def TV's can handle a lower-def signal (e.g. your 1080P set can handle a 720P signal OK) but NOT the other way around, then it is necessary that you feed one 720P signal through a splitter to both TV's. Now, I'm not so sure that the HDMI system and the TV's are smart enough to figure out which signal type a TV requires. I suspect YOU have to set the HDMI source to the 720P setting. If you set to 1080P, I expect the less-capable TV will display nothing.
IF you are feeding two different TV's from a computer graphics card, MAYBE there's another way, too. IF the graphics card has dual HDMI outputs that con be configured separately (like a dual-monitor system), you could connect separate HDMI cables to the two TV's, then use the video card driver configuration system for dual monitors to set each to its optimal output settings.