Compared to 509, the 590AXII tilts towards warm, but only by a smidgen. After living with it for a few months now, I would say the 590AXII is fairly neutral with just a hint of warmth. And as Eric said, the extension on both ends is really amazing.
I would agree with this post by Arafiq. Similarly I find the L-590AXII to sound very close to neutral, leaning slightly toward warmth. I have owned many amps in the past which include some costlier pre/power combinations and the Luxman L-590AXII is the first high quality integrated which I can live with for life. It may not be a Vitus, Gryphon or other uber-amps costing up to $30,000 but the quality really shows.
The Luxman L-590AXII sounds smooth, warm and natural whilst displaying good detail and a refined and nuanced delivery. The treble is smooth, detailed and illuminating without sounding bright or etched while the bass is very satisfying, showing good definition and detail. Basically a balanced reproduction across the frequency spectrum. I don't have experience with the L-509X but looking at your response I feel the L-590AXII Class A will better fit my Marten Duke 2 and listening preferences.