The number sequence next to the "T" indicates the diameter of the fluorescent tube in terms of 1/8 of an inch. Therefore a T12 is a 1.5 inch diameter tube, T8 a 1 inch diameter tube and T5 a 5/8 inch diameter tube. Each tube type has it's own ballast design so generally none of these tube are interchangeable. The ballast/tube designs each have their own efficiency and light output, the smaller T5 is generally being accepted as having greater output.
The advantages therefore depend on your objectives. If your objective is maximum light per unit volume then T5 is more desirable. If you wish lower light output, say for a low tech tank, then the other two tubes are better. Depending on vendor and brand the T5 system tends to be more expensive as well.