Luxman L505uXii or Hegel H390

Luxman.

+1, Luxman.  Of course, if possible, I suggest you audition both amps.  

No contest......I would go with the Hegel H390.  First: with the Hegel, you get a supremely powerful and high current/damping factor unit (that's built like a tank) that will even drive my power hungry, highly inefficient Revel Salon 2 speakers to astonishing results.  Forget about all it's other features for now, and know that as a stand alone amp/preamp, this thing is one of the very best sounding integrated amps on the market, hands down.  If I had a larger room, I'd go separates.  In my room, though, I didn't even feel the need to go with the more powerful H590 to drive my speakers.  The H390 is definitely a world beater and one of the true high value to performance unit on the market today.         

Depends on your speakers and your taste.  Both are excellent products but can't suggest one without knowing more.  

Tough choice--agree that it probably depends on taste and synergy.  It's kind of hard for me to imagine the lowest tier Luxman beating the penultimate Hegel.  I had the H390 and currently have the Luxman L-509X.  While I think the Luxman is the better and more natural sounding integrated, the Hegel comes pretty close on technical merits, and it just may be a matter of preference.  I heard the L-550AXii, and while certainly musical and enjoyable, I felt it lacked the depth, detail, and precision of Luxman upper end amps to a noticeable degree.