The press is one of the purest power moves in arm wrestling. If you are confident that you have superior upper body power (especially chest and triceps) to your opponent and are at least equal in bicep and forearm strength, this is a good move to perform.
The press is also a good move to use in a long tournament. Unlike the hook and toproll, which rely most heavily upon the biceps and forearms, the primary muscles used in the hook are the triceps, shoulders, and chest. Thus, a good way to give your bi's and forearms a rest during a long tournament is to throw in a press when you can.