As far as the differences in rewards go... if you're not taking in preps to a burning dungeon, you're still making less than just doing the PQI. If you take in preps, well... you're making significantly less than the PQI. What is hard to quantify is the "difficulty" of a random race/class/badge combo to assign it an appropriate reward (and in fact some are quite simple).
Bet on the Boss. Burning dungeon tripples the trophy price, so it tripples Bet on the Boss too, which puts you well above PQI. PQI also can end up with purist or cost actually more preps because you end up with wacky class combos
(ELF MONKS EVERYWHERE,ARGH).
Personally, I tend to ignore PQI for those reasons; Burning is easier and gives you more, and even without BOTB you only get 50 more gold on the PQI, for usually much less trouble.
At least the badge is never Vicious Token
Mentioning that, what about the Goatperson? Does PQI factor he/she/it in?