In terms of amplifier requirements, they are probably very similar. B&W recommends 30-300 W 8 ohms for both models.
The Amp 10 is rated 200 W 8 ohms, 400 W 4 ohms, given that the 702 S3's impedance is 8 ohms nominal, 3.1 ohm minimum, the Amp 10 is adequate for them.
All else being equal, mono block equivalent of the Amp 10, that is one that is rated also 200/400 W 8/4 ohms will be better as they are more "separate" than a 16 channel "separate" power amp. However, in terms of audible difference there will be none. Very few power amps will sound audibly better than the Amp 10, based on specs and measurements.
Marantz AMP 10 200 Watt x 16CH Amplifier Bench Test Results | Audioholics
You can of course BTL the Amp10 with the 702S3, but I would suggest against it, because I don't believe they are truly 8 ohm nominal speakers, based on the very similar 702S2, in case the S3 might have worse phase angles. That said, if you don't push the volume, say if you typically listen to volume setting below -15, then there should be no danger. How much current your speakers need depends a lot on your listening habit, that is, you seating distance, and your SPL requirements/volume setting, and use of room correction. Impedance is just one factor, and as you know it varies across the audio frequency band.
If you are really bothered by using a 16 channel amp jammed in one box, then okay, for super extra/ultra peace of mind, go grab a monoblock Hypex or Purifi based 500 W 4ohm power amp and call it a day. It's your money, so...
I will never buy a 16 channel amp myself, to me it defeats the idea of using separates, may as well use an AVR such as the Denon AVR-A1H lol... That's just me though, and I do believe monoblocks won't offer audibly better sound quality than the Amp 10, if the listening are told they are listening to monoblocks only in a blind test.