I don't think anyone can say the V6 Omega was a 'quick' car..... but what it did have was effortless power. I've only ever had Auto's (which is the best transmission choice for any lazy car) and the 'lazy' power was utterly brilliant. A steady cruise at 70, give the pedal a small nudge and you'd be doing 90 in no time at all.....
I can't see the various Poice Forces contining to use them for as long as they did if they weren't 'quick' or were classed as a 'slouch'. Most Forces I understand, loved them. But feedback from the Officers using them would have resulted in their earlier withdrawal from service if they weren't classed as reliable, powerful or quick enough for the job.
Depends what you are comparing them to....
Well, watching the usual Police programmes, the Omega was quite often used in chases around residential areas.... A Golf, Focus, even Astra of the time would out-handle an Omega, fit through smaller gaps, and probably be better overall.
As I alluded to above, the Omega was really a Motorway cruiser, and did handle high speeds very well. I've seen north of 150MPH in a couple of mine (private roads of course

) and you wouldn't even think you were doing 120MPH.
In-between my last two Omegas (a 3.0Elite and a 3.2Elite) I had a 535i V8 e39. The BMW was faster, handled MUCH better, was incredibly reliable, and if it weren't for a poor repair in it's past (rust crept in) I would possibly still own it. I've recently driven the 540i e39, and that's just another step ahead. (I'll accept that the Elite spec suspension is not designed to be thrown around, and the Police spec cars were more planted, but you can't adjust the chassis).
As for the Volvo's, never owned one, but did have a blast in a V70R..... sounded lovely, massive turbo lag, and with only 240BHP, (although quite a healthy torque figure) it felt a bit flat..... probably being a bit lardy.