The Beta lays a WIDE net of mines (group of 8, then 12 then 16 for T1, T2 and T3 respectively) that can hit multiple ships, be they above/below or beside you. The downside of it is they cover such a wide area and they cannot all hit the same ship (unless the ship flies through the DEAD center, which is unlikely).
The Alpha lays a trail of mines (2 groups of 4 for T1, 3 groups for T2 and 4 groups for T3) that are put out behind you about 2-3 seconds apart. This power is useful if you are trying to hit 1 ship with as many mines as possible. They are so close together in their groups that 85-100% of the time they all go to the same target.
I may have mixed the names up (alpha/beta) but thats what they do. I prefer Alpha myself, but Beta's good if you've got mines with a nice proc you want to spread around (i.e. Plasma mines, chroniton mines.) because it has such a wide area you can hit many ships with the proc.