Just heard the Avanti III for the first time at the NY hifi show. They were driven by Hovland amp/preamp and in my opinion offered some of the best sound at the show.
Others I have heard that rivalled the Avantis were: Coincident Tech. Total Eclipse, Gershmann RX-20 and their big egg-shaped speaker(forget model), Von Schweikert VR-5 or 7, Silverline Sonata or Sonatina, Joseph Audio RM33, Soliloquy 6.5 or 6.3.
Sorry for so many recommendations, but I have heard all of these and they are all impressive in their own way and competitive with the Avantis--and most of them cost several thousand $ less than the Avantis, which may be a consideration as well. At this level, however, it comes down mainly to personal tastes, associated equipment, and your room. If it were me and it were possible I wouldn't make my choice until hearing as many of the above speakers as possible, otherwise you'll never know. But hey, that's half the fun of this right? Best of luck.