I listened to a pair of Avantgarde horn speakers a while ago (one of the larger sets hooked up to some first-rate electronics, like their current Trio G3) - it wasn't honky-sounding at all.
Definitely worth an audition! You need a lot of space for that kind of horn speaker, though.
I listened to a budget set of Klipsch horn tweeter towers and they sounded weird for sure. Not "honky", but not great.