"One of the reasons I'm looking to upgrade is I need speakers that sound good in a variety of rooms because I move every couple years. For some reason I assumed the horn would have superior horizontal dispersion. If it's inferior to a dome that would give me less flexibility rather than more."
Its not really better or worse, as much as it is different. Horns just have a sound that not everyone likes. Its not room dependent either. Its no different than any other design. If you like them you can usually make them work, and if you don't no amount of tweaking will make it right.
If you're not sure about horns and you can't afford to take a loss, its worth mentioning that very few audiophiles actually use them. The largest subgroup, by far, are people that are into low output tube amps. They use horns because they're so efficient. Also, those amps are usually rolled off quite a bit in the highs, making horns much more listenable.
That said, you could be part of the group that loves horn speakers. Nothing wrong with that. My only caution would be to make sure before you buy a pair so you don't loose money on a mistake.