Both of them will die because of the lack of preferred nutrient.
Rhizopus and Aspergillus both are mostly heterothalic fungi that generally grow on decaying organic matter. Both of them have hyphae that grows into the substance of the organic matter and secretes enzymes that digest the organic matter and simpler nutrients are collected and consumed by the fungi.
As the Rhizopus is growing in wild, its adapted to a particular concentration of nutrients. When its plucked and put into an orange, the high concentration of citric acid and sugar makes the surroundings hypertonic and the fungus dies of dehydration.
In case of Aspergillus, when its plucked from the orange and put on slice of bread, aspergillus was adapted to the high concentration of nutrients and particular type of nutrients in orange. As its put onto bread, those nutrients are missing here and the Aspergillus can't find its food. So it dies.