I voted other. I don't think there should be fans in any stadium. Its simply not worth the risk. I get it for the players, they get paid to be there(also why I support no college football this season.) I also don't think they should do anything fan-centric or related, such as cutting to fans celebrating at home or whatever.
I'm actually really interested in being able to hear plays being called or audibles, and more of the battle before plays start. I think this could potentially be a really fun season for people like me, who are just as interested in the strategic battles from play to play, and not just who wins.
Along those lines I guess, I'm not sure I've ever cared about fans to begin with, at least from a TV aspect. They are just noise, usually more annoying than anything else. I've lived in Wisconsin pretty much my whole life, and very few things annoy me more than Packer fans, who have been drunk since 7am, just screaming their lungs out, seemingly always an inch away from a mic. Its been a little rough to watch basketball with no fans, but that is a more fan friendly sport I think, the fans don't overwhelm as much(probably due to 30,000+ less of them) and the shoes squeaking sound is a little distracting. I don't think fanless football would have those problems. Maybe you pick up some more swears, but that doesn't bother me at all.
To directly answer the question though, I really don't think home field advantage is a real big thing anymore. There was a time when it was, but I think that time has passed.