10 vs 12: A 12 inch subwoofer will provide more output, usually, with the same power. This is due to a larger surface area. We are also assuming each is in its ideal box. Low end response from a larger cone is easier to come by. Don't be fooled by the popular myth that "smaller subs are faster." There may be a difference in sound quality when an 8" sub's motor is used on a 12" sub, but with any quality manufacturer, there is no loss of "sub speed." (This concept is simply ridiculous, despite what the expert installers at Best Buy tell you.)
12 vs 12 Shallow: A 12" typical sub usually has more travel distance (xmax), is less expensive, and in some cases more efficient (louder with less power.) A shallow 12 is more convenient to install.