Checked a few of my Live Photos I’ve taken (by accident if I’m honest. I haven’t been a fan of the feature previously) and, yes, it looks Live Photos are now made of actual full res photos, or some compressed version of near enough full res photos, that the frame you pick is of full/near full quality.
Note: I took these on a 7+ with HEIF/HEVC enabled. YMMV
Edit: more succinctly I can’t see any differences between the default static picture and the other choices, other than those you would see between multiple manual pictures or burst mode. Some are better, some are worse.