I'd guess the Polk S15 plays louder than the BS22 with better bass. I know the S20 does and I would take that S20 over the BS22 any day.The 703 are very nice speakers that can be had almost as cheap as the S15 during various blowout sales. The S15, on the other hand, isn’t a good speaker, no matter the price. Better off with the BS22 if you want to go as cheap as possible.
Don't over estimate the Harman rating. It is fun but in no way is it a fact.
Many buyers will not like the BS22.
I owned the 703 for 2 years along with a dozen or so other monitor speakers to compare with. That speaker is superb. A very very nice speaker. The blowout is over though. Might find a pair for $800 or so new but the $400-500 blowout will never happen again. Still, they are worth $800. $10 bucks says Amir would love them as they have super bass.