I think they are very different, and liking one doesn't mean you'll automatically like the other. For me, Luxman is a bit 'meh'. Nice, beautiful even, but not very engaging.
Accuphase, however, is probably my favourite amp brand of the moment. Their current range can, as far as I'm concerned, do no wrong. As the name suggests, Accuphase take pains to preserve the phase relationships in the music signal, and this only really becomes apparent if you use their amps into speakers which also pay attention to this. Obvious ones are Avalon, Focal, Tannoy, and the new kids, Fyne Audio, but I've also heard them sound wonderful with Amphion and Russell K. These speaker brands all take trouble over things like time alignment, simple, phase-accurate* crossovers, and such like. I think an Accuphase amp through transducers like these is revelatory. What I take from them is an extraordinary capability with timing. Musicians seem to up their game, everything is tighter, cleaner, on the money.
They're also pretty bombproof. Their CD/SACD players are also pretty amazing. And, yes, I'm reliably informed their onboard phono stage is as good as you'll get for the money.
*Yes, I know, crossovers are not truly phase-accurate, but some are a lot better than others.