I have recently returned from a 15—day cruise with Regent, and I cannot say that I found the crew, or the staff, impersonal or cold. In fact I would go almost as far as to say that you could exchange the crew/staff from 'Seven Seas Voyager' with any Azamara ship, and you've be unaware of any difference.
I thought the entertainment better, and the theatre is certainly far superior.
Other things that Regent did better than Azamara: embarkation process; boarding, safety drill, booze in general.
Stuff that I thought wasn't as good: there was no decent English bacon (had to make do with Canadian); the showers in the standard suites are smaller than in Azamara's CC suites; and there are significantly fewer activities during the day.
Equal: although the menus are more imaginative the execution was sometimes quite poor; for me the 'vibe' was every bit as good as Azamara.
Having said this, I could never, ever justify paying Regent's prices. We got a last-minute irresistible bargain, which made this cruise exceptionally good value.