I've done enough Japanese jigsaw puzzles to now say that I believe Yanoman's may be the best. Outstanding, consistent quality; beautiful image reproduction; and an interesting variety of pieces all make for some wonderful puzzles.
Square Enix is up there, Epoch is quite good, Ensky is decent, and Appleone is all right, but the older Evangelion Yanoman puzzles are some of the nicest I've ever done.
Caveat: I haven't done a Beverly puzzle before, but have a couple in the ol' backlog. We'll see if they're as good as Yanoman's.