Most of us have separates, though a surprising number rely instead upon the integrated approach.
And integrateds have their charms.
For one thing, if the unit's designer focuses their efforts on sound quality (as opposed to just meeting spec, as is common), then the internal sub systems of that integrated can each be optimized for its synergy within the system. And, there are no interconnects.
On the other hand, a separates approach under the same conditions—designed by a team that focuses their efforts of sound quality, then I would put forth the argument that better performance will always be the case.
Why? Because separates are....separate. Separate power supplies, isolation from noisy components, a chance for each designer to really rock it out in terms of performance.
Integrateds are fine as well as convenient. I just think that at the proverbial end of the day, we're going to be happiest with separates.