Two Stereo Amps, Bi-amp or Monoblock?

From what I have seen, the normal step-up from a bridgeable stereo amp is to buy another and use them in monoblock format. You could however buy another and leave them in stereo and simply use one amp for both channel tweeters and one amp for both channel woofer/midrange. I understand that this is not a full 4 monoblock bi-amp configuration, but I wonder if the bi-amp advantage is glimpsed to a large extent in this format and perhaps a better sonic improvement over running the two amps in monoblock. Thoughts or experiences? Aside from sonic benefits of either, what is the resulting power increase from the two formats? In the "bi-amp" format you would also have the ability (or advantage) to offer a different amp to the tweeters and to the woofer/midrange; whereas in the monoblock you would need to match the amps.