The specs are slightly better in the bic but neither one will do what you want. For HT neither one goes low enough, and your room is too big for a single 12”er. Especially if it’s open to other rooms.
I’d buy 2 of these and be done.
https://www.parts-express.com/dayton-audio-sub-1500-15-150-watt-powered-subwoofer--300-634
You’re definitely working in a tough price range, but for that money I’d buy the Daytons all day long. Klipsch isn’t known for great subs, and bic has a decent reputation, but only in the budget realm. FWIW,
@Reckel, a member here, has QTY-4, BIC pl200 for sale. Can’t remember what he wants but it could be worth asking him.
Edit: also, don’t get too caught up on the specs. Third party reviews and measurements ore much more meaningful, as manufacturers can fudge specs. For example, the 150w rms rating on the Dayton’s might seem small, but considering the driver is 56% larger it has much less work to do to get the same output. Basically they will outperform either of the aforementioned subs. Keep in mind as well, subs are “systems” that are designed to work as such, and efficiency and design can easily outweigh inflated power numbers.