Recovery has nothing to do with gender.
Generally speaking the person who got dumped has the hardest time recovering. One exception might be if she or he were caught cheating or committed some other "deal breaker" in the eyes of their mate.
In that scenario the (betrayed person) ending the relationship is more likely to need more time to recover from the breakup even though they initiated it. Whomever is "caught off guard" by the details leading up to breakup tends to take the longest to recover.