What I thought when both where here was that Mesko was more accurate. He was better at getting the ball so that it rolled out before the end zone, or having it bounce back so that it didn't roll into the end zone. Allen on the other hand had a much stronger kick, but they tended to not be as accurate. But since then Allen has kept his much stronger kick, and become much more accurate than he was before. So now we get long kicks, that are really well placed so they don't become touchbacks. He can also give kick really long balls, with great hang time so our gunners can force the returner to make a fair catch.
Belichick really made the right decision. He went with the guy that was slightly worse from the start, but with much higher upside, and that payed off.