1st things first, your room is not large.
As a general proposition the smaller the driver the faster it can respond to changes (i.e. tighter bass). The smaller the driver the easier it is to integrate at a higher crossover lever. A good sub with a 12" woofer is usually easier to use than one with a 15 inch but won't go quite as low. A lot depends on the bass quality/quantity of the main speakers.
For example, if your main speakers have great bass down to say 40hz and you just need the bottom octaves you could use a 15" sub, but if your main speakers need to be rolled off much higher up you would probably be better off with a 12", or even better yet a modle with two smaller drivers (potentially even faster w/same volume capabilities.)
As a general proposition the smaller the driver the faster it can respond to changes (i.e. tighter bass). The smaller the driver the easier it is to integrate at a higher crossover lever. A good sub with a 12" woofer is usually easier to use than one with a 15 inch but won't go quite as low. A lot depends on the bass quality/quantity of the main speakers.
For example, if your main speakers have great bass down to say 40hz and you just need the bottom octaves you could use a 15" sub, but if your main speakers need to be rolled off much higher up you would probably be better off with a 12", or even better yet a modle with two smaller drivers (potentially even faster w/same volume capabilities.)