I think, in your situation, yes.
A middle-ground compromise would be to get the upper end 10" with the less expensive but more powerful amp Stinger amp. In order for the RS-SB10 to perform at the volume of the 12 (at the same 300 watts), it'd need substantially more power. Since the 12 in this case the SS-SB12 can't handle the power the other can, then yes, up to the rated power limit of the SS-SB12, it will outperform the 10. Since either of the amplifiers will exceed the capability, then it becomes a matter of price-to-performance ratios, sound preferences, and ultimately, need. The 10 is a better sub and you pay for it. From what I see regarding your listening preferences, I don't think you're ever going to put 500 watts into any sub - that's really LOUD! if you think you would, then the rest of the system has to be re-evaluated too. At some point, the sub will drown out the other components unless they can keep up. With that in mind, you might ask, why either amp? IMHO, it's always better to have spare power and room for the amp to breathe. Headroom is a must in subwoofer applications. I am currently running a 3000-watt amp to dual SEALED Focal 33v2's, running them at 4 ohms to the amp which is rated to put out roughly 1500 watts at 4 ohms. Wasted power some would say but not to me. I'd rather the 1 ohm-rated amp run cool and easy at 4 all day long instead of running at the peak, even idling. While MDF is the preferred box material, the poly-box is waterproof too. Where do liquids go when spilled above in the seat? Pros and cons to everything. It may have been needed to get the 12" into a cavity that was large enough as well. I'm sure that Alpine is aware of the differences in sonics too. One thing they do well in good plastic fab boxes is engineered rigidity (Ribs and braces) that you just can't duplicate in a wooden structure as small as these. I would recommend that you buy a pound of Acusta Stuff and put 1 lb of it per 1 cu ft of airspace. (if these equal a cubic foot, then one pound of fill. It will help in either case.
Acousta-Stuf Polyfill 1 lb. Bag Speaker Cabinet Sound Damping MaterialAcousta-Stuf, a synthetic material made from crimped fibers, is an excellent choice for filling or stuffing small enclosures or transmission line cabinets. Long fiber wool has been a favorite among serious speaker builders but...
Some will argue that it doesn't make much difference, I say it makes a LOT of difference in especially compressed boxes such as these.