I suggest that the first step for you is to try to figure out why this is happening; perhaps by trying different ways of putting them to bed. Have you asked them what is going on. They are young but may be able to give you some clues. Do you know what happens before the youngest gets out of bed?
My daughter tried to get her two to sleep in the same bed; a king size bed. They would either play with each other keeping both awake until one wore out and fell asleep. Or they would settle down and be almost asleep and the other one would move and kick or knock into the other one; waking them both up. This sometimes happened after both were asleep. The older one would go to her mother and complain loudly or the younger one would loudly cry.
She put them in bunk beds and it seems to be working. They still play off each other. For the first few nights she had to go in and tell them to "knock it off" because they were continuing to giggle at each other or fight even tho they were in separate beds.
They listen to music or a story on CD which helps to keep them calm. The tricky part is remembering whose turn it is to choose. If I were her, I'd make the choice and elimanate the "battle."
Have you tried putting the beds across the room from each other? Did you do a transition "ceremony" for the little one when you switched him to the big bed? Does he, perhaps think of the bed as his big brother's bed? Could you put the youngest one to bed first and then the oldest once the youngest is asleep. This could be a perk for the oldest. ie: "you can go to bed a bit later if you let your little brother sleep."
I also agree that shortening or eliminating the nap may help.