Which active speaker for under $650.

Look at the new Emotiva Pro series. The 6" version($799.00 a little over budget) blew me away at RMAF. Huge clear sound with 210 amps in each speaker. I may buy a pair for a porch system.

Look into the self-powered KRK Rokit series, whichever would fit your room size and budget. These are very musical speakers, not edgy like many inexpensive monitors. The founder of KRK is an audiophile.

Note that prices are per speaker, so the closest to your budget is the 8" 2-way Powered 8 G2, which is bi-amped with a total of 90 watts rms per cabinet. I've heard 'em and they sound excellent. You can hear them in the pro audio section of any Guitar Center. You may want to bring your own source material to audition or you'll probably be stuck auditioning with obscenely compressed mp3's of dance mixes.

I've never seen the advantage in powered speakers over passive. I DO understand the advantages of an active speaker... one with amplifiers tailored to each driver, and incorporating an active crossover.
I do have a pair of Revox Agora Bs which use three 100wt amps pr speaker - One each for tweeter,mid,and woofers, and the advantages in power, & clarity are appearant. I've seen "powered" versions of conventional speakers, but never understood the advantage. How are speakers that will require a power cord and low level input more convenient than "conventional speakers that only need a high level signal? I don't see any performance advantage, so I'm assuming some find them simpler to use?
This question comes from a steady electrostat proponent, so I'm used to having to deal with power cords at each speaker, but I don't see them as more convenient.

BTW, this isn't meant as a condemnation of your wish for powered speakers, I really have always been curious as to why they are popular. FWIW, I have listened to the Quads, powered & not, and think they are very nice... being a Quad esl user for over 25yrs, I'd lean towards them if I were in your shoes. Though, I'd get the unpowered version LOL!