It's more profitable because you set the price. You can set it higher than expectations. The renter might be mining some alt coin in hopes of a pump and dump. The renter might be using your gear to solo mine and hoping for a 25BTC hit. Who knows what prompts their behavior...
How much do you earn with MiningRigRentals during periods when rig is not rented out?
Depends on which pool you set your miners to mine on when not rented. When not rented, they behave as any other miner on whatever pool you've chosen, and hence all typical things apply (like fees, etc).