I would vote for separates, but having in mind that one will ususally spend more and it will take more time to get everything ’right’ You will need more cables, including power cables as well and more time to make ’right’ choices, between components and cables.
Even the higher class integrated amps are often not a match for a separates that might cost the same, or worse, there are very few integrated amps at all, that can match the 10k separates bought in Sh, for example. That amount of money, in sh, can get you far, meaning it will give you more than almost any integrated amp, without the cost of cables.