10" woofers are not faster than 12" woofers. It is a common myth. The fact is, that a 12" woofer has more output than a 10". It also playes deeper due to the increased surface area. What you are experiencing is the subwoofer running too hot. Meaning the level is too high. Deep bass at a high output level will always sound "boomy". Have you ever just listened to a subwoofer with no midbass, mid, or high range playing? They all sound very similar for the most part.
See this link for myths with subwoofers:
http://www.audiopulse.com/know-how/subwoofer-driver-guide/myths-about-subwoofers/
Midbass is usually the weakest link in a car audio system. Many people put in a few subwoofers and amplifiers and just replace factory speakers with basic coaxials. Some may run an amplifier on these to help but very few treat the acoustical space around the speaker properly. Even fewer people design proper enclosures for their midbass drivers. Much of the "speed" and "quickness" that car systems seem to lack is due to this issue. Proper enclosure design for the car is the same for home audio. T/S parameters must be used and modeling needs to be applied to identify the correct enclosure.
The fact that the car audio environment is very conducive to bass amplifies the effect of having more bass capability than midbass, mid, high range.
If a 10" woofer were quicker to return to it's original position it would be playing a different frequency altogether. 60hz is 60 cycles a second. If a woofer moves any faster or slower than that, the frequency changes.
If your crossover is set to 50hz low pass, what is the slope? My guess is that because you have such a low crossover point the lowest frequencies are quite loud causing a "boomy" sound. You system has a general lack of response in the critical 60hz-200hz range resulting in your problem. I would also guess that you do not have dedicated mid-bass drivers.
Gain controls on car amplifers mean nothing as to how much they are "turned up". It is possible for a car amplifier to make full power at 0 gain with a high voltage output deck. What kind of head unit do you have? What is the output voltage? What is the input voltage range for the amplifier?