There are some differences in meaning when you change the placement, mainly in emphasis, but for your actual example sentence it doesn't change the essence of what's being said:
A) Jake's number of match wins while playing for Australia is greater
than the number of match wins any other player has gained for the team
that player belongs to.
B) Jake accomplishes match wins for Australia more often than any
other player does for the team that player belongs to.
Because getting wins for your team more often than anyone else is the same thing as getting a greater number of wins for your team (because if you win more often, it stands to reason that your number of wins will be greater) the two sentences mean the same thing (As Adam Martin pointed out though, sentence B is an unnatural and awkward sentence structure and should be avoided if possible). However, in a different context, this may not have been the case. Consider:
C) I have eaten more biscuits than anyone else in my house has. (My total number of biscuits consumed exceeds that of any of the other people living with me)
D) I have eaten biscuits more than anyone else in my house has. (the number of occasions on which I have eaten biscuits is greater than that of any of the other people living with me, but I did not necessarily eat more biscuits than they did on those occasions).
As you can see, in some contexts [verb]ing more [noun]s than someone is not the same thing as [verb]ing [noun]s more than someone.
As for the question of which teams were being referred to with "his team", pronouns like "his" refer back to the last subject mentioned, which in this case is "any other player".