Are integrated amps technically better than separates?

But also, this is very brand specific. Not everyone uses large, boutique caps at all. 

I agree. However, I am of the impression that large, boutique caps are there for better sound quality. 

What about the Integra separates?  I want to have more of the “movie theater” sound and power so I have been debating getting a more powerful system.  Should I spend the $$ on separates or on a nice sub woofer?  

I don't remember where I read it but some amp designers actually think that the best thing is to have an integrated amp with a separate power supply. That is a two box solution but with different separation of what goes in which box.

Another solution could be four boxes, pre and power and then separate power supplies for each. It may be technically better but it is very expensive.

HI,
Technically yes and no. Some of the advantages are shorter paths and same vibration across the unit.
Market wants to sell seperates for profit and integrates for share. Value wise an integrated unit is hard to beat. Consider what is required as accompanying material for preamp, phono, power, transport, dac and then prey for compatibility.
Market has plenty to offer and with careful matching of amp, speakers and room size you are close.
Seperates have the more potential but demand more patience.

When I am in my more involved phase I seem to go with separates for the fun-aggravation factor. There are more variables to consider and more components, cables And cords to swap out, mix and match. Matching separates can be a double edged sword. The “ what if?” factor can easily turn into the “ why did I?”one in this wonderful hobby.