What a rebel!
But seriously, I am in Arizona too--and maybe you run with your dog at night or around dusk/dawn--but the iPad is not very good in the bright Arizona sun. In fact I'd say the iPhone is marginally better in that respect.
Now regarding running while recording video, I think more than looking silly there is the issue of holding such a large ungainly device while doing it. I can't imagine doing it one-handed.
As for viewing iPhone 4S videos on the iPad the camera connection kit is great for that. But you do need to have it and a sync cable with you to go straight from iPhone to iPad.
Michael