Is "Yes" a clear enough answer?
Having said that, good bass is mostly in the speaker, however, If you are underpowering your sub, it won't push like you want it to. Make sure the amp is providing enough clean power, and if you don't have enough bass, upgrade to a bigger sub, or add another one.
And be careful with "upgrading" to a newer version. Many of the formerly great car audio powerhouses are making cheap junk these days. Having said that, I doubt you'll hear much difference between a P1 and P2, unless you step up a size or two.