The biggest home run list is so incredibly difficult to rank after the first one.
Carter has perhaps the biggest hit in baseball history, let alone Jays history, so that's easy.
Alomar's home run, as some have already said, was the ice breaker that led to 2 Championships. Do you take that into consideration or do you just look at the moment? It didn't give us the lead and it wasn't a game 7. In that game, he also went 4-5 and made a game saving defensive play, which plays into the lore a bit.
Bautista's home run was easily the most electric/epic of the three (perhaps some recency bias there), but it was also the least important in some ways. I've just never seen anything like the atmosphere and reaction. That goes for any game, not just Jays games. The Rangers throwing at our players, the perception that we got cheated on the Choo play, the length and buildup. It was really something to behold.
Springer's home run is probably more important than Alomar's without the benefit of hindsight. If we win the World Series, I think it goes to #2 for me, but that remains to be seen.