I have listened very carefully to both. The Zu Omen has lower bass extension. For example the 1812 Overture canons sound very impressive with deep, dynamic, tight bass. Where they tend to be a bit rough is on the intricate details and clarity of certain genres of music such as jazz and classical. They tend to lack the finesse. They have a sort of rough sound quality to them in the highs and mids and don't quite produce the intricate details of the music IMO. We compared them to a pair of B&W 601 S3 and the 602 S3. Incredibly the only thing the Zu's did better was play louder IMO to impractical party levels.
I suppose if your biggest interest is to rock out like Led Zeppelin, Van Helen, Rage Against The Machine or TOOL for example and you are not really into jazz or classical, they are fun in the rock department. They play really loud, are efficient and would be amazing for a party. Out of them all, I absolutely love the Heresy the best. I've had mine for about 2 years so far and wouldn't trade them for anything. Since most audiophiles play their music flat, the Heresy won't extend to the deep bass because they were primarily designed as a high and mid speaker for the mighty Klipschorn. I think audiophiles have fallen in love with the Heresy for that reason. They are not a boomy bass kind of speaker and when you hear voices like Ella Fitzgerald or Patsy Cline, they are simply unmatched. Trumpets and horn instruments Like Sonny Rollins, John Coltrane, Louis Armstrong and Miles Davis sound super organic, very detailed and extremely lifelike! Even intricate, classical guitar like Segovia sounds heavily dynamic in the Heresy. For piano I enjoy Bill Evans. The sound is to die for.
The only thing the Omen did better IMO was deep bass. Other than this, the Heresy was much nicer IMO all around. I later added two REL T5i's to my Heresy and once I got them set correctly, my jaw hit the floor. Music from Hans Zimmer soundtracks like Interstellar, Batman Begins and Blade Runner for example are off the scale! When you play huge orchestra like Karajan Verdi AIDA, it's sound like a HUGE wall of sound hit you. I only listen to stereo and use tube amps for everything. As long as you couple the Heresy with a really good amp, you will get a nice sound. IMO, if you drive a bad amp into them, they will bring out the bad. Like one reviewer said, they will shine a spotlight on any inferior recordings. 100% I prefer the Heresy.