As far as my personal experience goes:
For symmetric cores,
the more speed dominant you are, the less difference it will make in the ball reaction.
The more rev dominant you are, the more difference it will make, maybe to the point where it will just barely be observable.
For asymmetric cored balls,
The same is true, except for rev dominant bowlers, side/top weights seem to make even less difference, even for rev dominant bowlers.