The "taking less money" argument has been thrown around a lot, but I have yet to see any proof to this. The offer that the Lakers had on the table was a 4yr/$36M deal with the 4th year being a team option with a $3M buyout. That means that Odom is only truly guaranteed to make $30M over three years with the Lakers. Now it is speculated that Buss will offer less than that. All of the other offers that have been tossed around are only speculation, and many with knowledge refute most of them.
He would be guaranteed to make around $35M over five years with the Heat. He would also be able to start and perhaps make even more money by displaying his talent, since years 3, 4, or 5 of his Heat deal would likely have a player option. When you consider the money that he would save on cost of living and state income tax deference, I don't find that it is overwhelmingly evident that he would be sacrificing much money.