Integrated versions separate subwoofer

My GENERAL opinion is that an integrated unit may be better if you have the space. Couple reasons:

- Physical placement is within the same "space" as the speaker, and there are 2 of them

- They are DESIGNED to be integrated well into the speaker

Again, a general statement, not perhaps universal. Integrated woofers may lack in deepest bass and air movement, something outboard sob's are especially made for.

Quantity or quality (or very high price)...

Go to a store and compare the B&W N805 with a sub to the N803 or 2.

Chams_uk I see. So a really crazy audiophile move would be to have a crossover for anything under 55hz and run that to a dedicated subwoofer, and also have integrated subs in the speaker.

No .. there's no concensus.
If your listening room is small a separate subwoofer can give more flexibility in placing the main speakers for imaging and the sub for optimum bass loading.
Either way good deep bass is quite expensive. If you get a separate sub then these cost $1000 up. If you want deep bass from the main speakers you'll need a much more powerful amplifier and physically large speakers.