I ran my guild through some experiments, and it seems that while difficulty doesn't affect the level of prizes, sticking to one opponent does.
I had people fighting a different opponent each, some fought the same opponents for the same week non stop, some changed opponents each day, and the people who stuck to one opponent for the whole week received better prizes. I only had around 15-20 people helping me out with this though, and it doesn't really seem logical as to why this is happening...
Maybe it's got something to do with the number of battles you accumulated with the opponent. Or the higher your score is with that opponent, the more chances of dropping better prizes.
A totally baseless guess, though. Could be completely coincidental.