Luxman L505uXii or Hegel H390

Both are fine amplifiers, but you are comparing apples to oranges.

What kind of functionality do you need. The Luxman is more on the analog side, or somebody who has multiple sources. The Hegel is more on the digital side with its built in DAC and digital connectivity.

Do you need the tone controls, on the Luxman. Do you need the power of the Hegel.

You need to give some thought as to what you expect or want out of each.

As for sound quality - no comment.

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.