I agree that the picture itself has no difference that I can notice.
There are some things other than picture quality that may influence your use.
I have a TV and Blu-Ray that are both Panasonic. When I connected them together with HDMI, they negotiated settings (1080i vs 720p, for example) to give the best picture. I didn't have to do any setup. I was able to override what they chose, if I wanted to, but the settings were what I would have used anyway.
Likewise with settings, they can operate each other's power over HDMI. When I turn off my TV, the Blu-Ray also shuts off (I know it's not the remote, because it also works when I cover the receiver or manually turn off the TV.) When I put a disk in the Blu-Ray, the TV turns on. I'm not too lazy to push the button, but it's interesting that they do this.
If your receiver goes out, your TV can play through its internal speakers via HDMI while the receiver is at the shop.
Something a little less wonderful is the high def copy protection. My StarChoice / ShawDirect has component and DVI outputs for high def. My TV will not accept the DVI signal (though a converter cable to HDMI), and puts a big message in the middle of the screen about unprotected HD. I had to connect the component outputs directly to my TV.