If I had to choose I would have to say like Eric Alexander when asked what is the most important part of a speaker, "Everything!" Its simply not true that the preamp is more important than the amp, or vice versa. Ditto speaker, speaker cable, power cord. People ask all the time what should I get a better turntable or cartridge? If all you care about is immediate impact on sound quality then it really does not matter.
Where it matters is money and longer term plans. Where money comes into your question it is really, really hard to find separates that all together will sound as good as a really good integrated amp- without spending a lot more money. Its not that separates can't be better. They can. At the very highest of the high end its probably just about all separates.
But at the level of us mortals with very finite funds you will find it is probably impossible to beat something like a Raven Blackhawk at $3800 with any combination of separates under I am gonna guess and throw out $5k. Although it could easily be twice that. That's because the most expensive part of any component is the chassis, face plate, knobs and stuff. Next to that is power supplies. The first is cosmetic but the second makes a huge difference.
So the separates designer of a $5k preamp has to budget a grand for a faceplate that does nothing for sound. Same for the amp. Integrated designer only budgets the one time. That's a cool grand he can plow into quality caps and stuff that actually makes a difference. People can argue but all they can do is plug in different numbers they can do nothing to change the fundamental math of it costs way more to make two boxes than one.
Then when you get the two you need to budget for a quality interconnect, something you don't even need with an integrated. People like to forget about that. But its part of the total. Ditto power cord, cones or springs, fuse, whatever you use to make it better, you just need more of with separates.
Its really no contest, not even close, at least not until you get up into the very high end with well into five digit price tags- and maybe not even then. We have a guy around here willgolf who has the funds and travels the world and the one he seems most smitten with is the Raven Reflection MkII. That's the one I have my eye on. Prima Luna would be a contender were it not made in China but even if it were made here it doesn't seem to be at quite the quality level of Raven.
https://youtu.be/Gcd76DZmbdY?t=112My views on this (integrated vs separates) aren't all technical arguments. I actually was looking for separates and had spent a lot of time searching out a good combination when a dealer friend suggested I try an Aronov integrated. Wasn't even considering a tube amp let alone an integrated and was really surprised when it sounded better than the McCormack DNA1 that was the best amp I had heard at the time. Then when I realized I could sell the McCormack for almost enough to buy the Aronov, and then not have to buy a preamp at all, let alone interconnect, power cord- it was the most no-brainer ever.
That was a very long time ago. A lot has changed since then, and a lot of my thinking on things has changed. But not on this. And check out that video. Can you believe this guy is so obsessed he uses three different high end resistors and even different solder? Incredible!