Short answer: Business school professors tend to have higher level contacts in industry and government than professors in other fields. So if they are 1) consulting, they are likely reporting to higher level executives who will pay them better, even for similar work.
2) For the same reason, a business school professor who leaves Academia for a full time position in industry is likely to leave for a higher level, higher paying job outside. Some of my finance professors took jobs on Wall St. Some of these jobs are available to mathematics people also, but "finance" and "business" gives one that extra edge. And a large part of this stems from:
3) Teaching MBA students isn't necessarily more demanding that teaching other students. But these graduates tend to rise to positions in corporations with more authority (and often more pay) than non-business engineering and science graduates. If one of your students from twenty years ago becomes CEO of his/her company (and this is more likely with business school than technical students), well, you get the idea.
Some of my own business school professors were either former or future "C" level executives (Chief Operating Officer, Chief Marketing Officer, Chief Financial Officer, even a CEO or two). The ones that left industry became professors because they grew tired of the "grind" and took a pay cut for a quieter life. But if it were too much of a cut, they wouldn't do this. The ones that left Academia and went to industry did so because their pay was a lot (not just a little) higher than that of say, a department head in a university with comparable authority and/or prestige.
In this connection, it is noteworthy that Arjay Miller was one of the "Whiz Kids" who took over Ford Motor Company (he briefly served as President) before he became Dean of Stanford Business School.