Why choose a round-head shakey head jig over a football-style jighead? 

What will the round style do that the football-style won't do, and why would it be preferable? 

Is it the same principle as jigs in general, where a  football-style head might be better for structure, while a round-style might be better for docks, etc?

From my understanding, the round ball head shakey head jigs tend to roll over unless you are using a high floating plastic. The football head shakey heads provide a base for sitting upright on the bottom. Think of a football head as a lineman doing a three point stance. Also football heads come through rocky areas better because they dont get wegded into cracks and holes. I guess the round heads are for structure and cover so you can work it through easier. I prefer the football head type and love the Shake2 jigs by megastrike. Hope I cleared some things up for you.

See, that's kind of what I was thinking.  It seems like the football head style would work better under most scenarios when you would use this method.

I'm just wondering when an angler might choose a ballhead over a football head-  I mean, they make 'em, so there must be a solid reason, right???

Your suggestion follows my train of thought exactly- just wondering if I was off base.

Nah you are not off base.  I think that the round head jigs would be better suited for grassy, weedy areas so they wont pick up as much crap as say a football head.