Hey just curious... Which other speakers are you runnin with the sub.
That will probably help you decide as well. Just an after thought.
I agree; it should have been the first thought, not an afterthought. If you're matching sub(s) to small stand-mount speakers with 4 or 5" woofers, dual 8" woofers would be a better match, both for speed and dispersion. If you have near full-range floor standers with dual 8" woofers or a 10", then you'd want one or two 12" or even 15" subs.
I have a pair of small floorstanders that use 5.25" woofers. They don't produce much meaningful bass below 50 Hz, especially in my living room which is open to the rest of the house. I augment the bottom with two 8" powered subs. They're sealed, but have dual passive radiators. There's still not much bass below 35Hz, but they provide extension to cover bass guitar, tympani, concert bass drum, etc. The best part is that these subs are very quick and blend seamlessly with the mains' 5.25" woofers.
Two 8" subs have almost the same radiating area as a single 12", but the 12" will reach lower but may well have a slower transient response owing to the larger diaphragm. However, if you look at the driver designs of JL and SVS, they appear to have the magnet strength and structural rigidity to have excellent transient response.
So really, the answer to the OP's question depends on the frequency range and output of the stereo speakers relative to the size of the room, and which part of the low frequency range you want to augment.
Take a look at SVS Sound's dual subwoofer packages
. One or more could fit your needs and budget. They have a dual 12" pkg in sealed enclosures that's below your budget and a dual 12" triple-ported design that's right around your budget. The cool thing about their triple-ported design is that they include three port plugs so you can choose from four different bass alignments for damping and room-matching. Instead of either-or, here's a source for dual fast 12" subs that would fit your budget.
Disclaimer: I have no affiliation with SVS or any other sub maker or dealer. I have an audiobuddy who has an SVS sub mated with his Magnepans and that's the extent of my personal experience with that brand. I personally own 5 Mirage subs and have a matching pair of Mirage MM8s augmenting a pair of Mirage OMD-15s.