Separates or Integrated? What makes more sense?

No right answer other than you must go listen to the components. Period. End of story.
Today I listened to Primaluna Evo 400 integrated. Very nice. Then I listened to the Evo 400 Preamp with the Evo 400 Amp, major difference in soundstage, black background and tonality.
I've heard the Ayon Triton III integrated and it sounds every bit as good as the Primaluna separates. To me.
By the way, there's no mandate to spend anywhere near $3k on an interconnect(s).

Goodluck and most of all, have fun

For 10K, I think I would have to seriously consider separate’s. Hope to get lucky and find some used or demo Luxman gear. 

At $10K I would go integrated.  There are some integrateds that are as good if not better than their separates counterparts (like Luxman 509x vs c700 combo).  Huge bang for the buck.  I spent quite a while trying to find a good amp/pre combo and the ones I liked the most were well over that budget, but that’s me.

You also save in cables, not to mention spending a lot of time and money playing with pre to amp cable synergies.  Though that is part of the audiophile adventure.

Even on the very high end, I have heard some absolutely amazing integrateds, like Gryphon and Vitus, that at times can match, if not beat, separates.  

Not to say there aren't some really nice integrated amps out there but in my present system my power supplies for the preamp and phono pre are separate. The makers of these probably wouldn't go to this trouble if it weren't a step up. I mean I guess they could take this approach for panache but they probably are more concerned with performance.
When you locate the power supplies in the amp box with preamp, and power amp and in some cases phono pre it would seem to present a problem with noise, something my system with high efficiency speakers is particularly sensitive to. So separates it is for me. The longer I'm in the hobby the more aware I am as to the importance of the power supplies. For the more knowledgeable designers of equipment on this forum, it would be nice to hear your honest appraisal of the significance and differences involved in isolation of the power supplies, benefits and drawbacks.

dentdog is correct. Isolating a preamp from a power amp in the form of separates will pay much greater dividends than any cable or power cord improvements. In fact to suggest otherwise, I think, shows a pretty glaring lack of knowledge regarding significant fundamentals. 

I know of no integrated amps that compare with separates made by the same company. Look to Gryphon or Vitus as examples.