"I absolutely love her!" = It might mean love her as much as is possible
"I definitely love her!" = means that I'm sure I love her, but it doesn't indicate how much.
Definitely usually has more to to do with certainty, and absolutely usually has more to do with amount.
"I absolutely hate this band, and I'm definitely sure I don't like them" = I hate this band the most possible amount, and I'm sure I don't like them."