In my experience the Korean models are decent quality and low priced. ESP is a bit more expensive and Jackson is competitive in cost. But I think what makes Ibanez attractive (aside from wylde1919's comments) is that a large number of influential endorsers use them. Steve Vai, Joe Satriani, George Benson, Korn, Incubus (acoustics), Offspring, Staind, System of a Down, etc. I also think the lack of custom shop with everything also makes the professional customs more desirable.
I personally like their innovations: All access neck joint, wizard necks, Lo Pro Edge trems, Jems and Universes, etc.