I am narrowing my choices down to

Rockville RW10CA 10" 800 Watt Slim Low Profile Active Powered Car Subwoofer Sub

BLAUPUNKT Blue Magic XLf 200 A 300-Watt 8-Inch Low Profile Active Subwoofer System Black

I also welcome recommendations

But I also heard this - Separate Amp + Subwoofer will always be more powerful than a powered subwoofer

But I also heard this - " Separate Amp + Subwoofer will always be more powerful than a powered subwoofer " do you agree or disagree? By the way I need as much space as possible, and therefore, Powered Subwoofer is the right choice for me.

Wife uses this in her SUV. 150 watt amp in it. Goes good with her caddilac sound system.

Kicker

The boys in my high school just put vibrating things under their car seats and told people their sound system was just that awesome.

I'm afraid I can't recommend any subs for cars, especially under seat low-profile models, for under $300 USD. It is a very inflated, rather dishonest market. Most of them either outright lie or misrepresent output wattage. Think about it... do you imagine an amp supposedly rated at 800 watts could work on a stock auto electrical system? Imagine how long your battery could run 8 x 100 watt light bulbs. Most incandescant auto headlamps are under 60 watts so perhaps imagine running 12 to 14 of those. No way your alternator could keep up.

How it is usually done is by 2 methods - Switching power supply conversion so one is not limited to just 12VDC and PWM digital amplification that measures instantaneous bursts lasting microseconds as if that was in any way comparable to actual RMS power. It's basically advertising hogwash.

Your best bet is to trust a company with a good reputation and decent consumer feedback (more comments is better) and just forget about most specs. Gear made in China is a crapshoot. Some are quite good and some are very bad, and few have decent recourse if you are unlucky.

More to the exact point, I don't really like either of the models/brands you posted (Blaupunkt is no longer "German Engineering") but if I was forced to choose between those 2 only, I'd likely go with the Rockville despite the fact that I hate it that they advertise 800 watts. If you could spend around twice as much, Cerwin Vega is OK and at least they and outfits like Pioneer are somewhat honest with specs.

BTW there is no truth to "Separate Amp + Subwoofer will always be more powerful than a powered subwoofer ". There are advantages and disadvantages (tradeoffs) to gear built both ways and broad generalizations are useless.

Thanks a lot, enorbet. Powered Subwoofer below the seat is the right solution for me because I need the trunk space. It is a working car.

What do you recommend? I listen to movie soundtracks, 70s 80s 90s music, and I read very positive reviews on Alpine PWE-S8

Price is no longer a concern. It does not have to be around $300USD

The Alpine PWE-S8 is an excellent value, well constructed, not bad to install. I didn't mean to put you off on the Rockville since they are making quite a name for themselves and make good gear. It is a highly competitive market and they have run the gauntlet and managed to not only survive, but thrive. Alpine has a LONG history so either should serve you well. I'm an EE so I just hate all the overblown hype advertising crap that seems to infest the car audio world, but that is the environment and if one wishes to actually sell some product there is a lot of pressure to "wrestle with pigs". That's why I qualified it by saying go with reputation not with specs.

Also, subwoofers are quite subjective beyond base considerations like reliability and ease of installation. Some people like earth shaking bottom end that can kill large mammals at 30 feet ( ) while others prefer audiophile level tight accuracy. Personally I rather like the tight sound of JBL and most Pioneers but I have heard some Rockville and Alpine as well as Fosgate systems that are setup right that sound really great but others of the same exact model that sound phony to me. With smartphone controls becoming ever more popular, setup REALLY matters.

You would probably like either the Rockville or Alpine models you have mentioned. I'd say go with which one you know fits your car size well and has the best setup options, but above all will suit your most loved music styles. HipHop fans like different subs than Classical lovers. That's why setup can be so important, a lot more important than advertised wattage. Be certain your car has a decent size battery and alternator. High power amps pull a lot of amperage when confined to starting with only 12VDC.

It seems like you have researched quite carefully and now that you've expanded your financial range of consideration, you are far less constrained. I'm confidant you will get one that works well for you. Good fortune!