There is no question. It's one of the pillars of Dominion rules: When given several options, you can always pick any option. (Otherwise Torturer would be... something entirely different!)
But you can't choose to gain an Estate with Workshop if the Estate pile is empty. The wording of Tournament implies that it's the same (it's "gain a Prize or a Duchy", not "gain a Prize or gain a Duchy"), although the FAQ is pretty clear on this subject.
The issue here is in how specific the instructions are, and how you can follow them.
If you play Workshop, you have to complete its instruction, which is gain a card costing up to 4. You must gain a card if able, and if there are no Estates, you pick something else.
Tournament specifically names two choices you can make, you can either gain a Duchy, or a Prize. You pick one, and then you try to do it. If there are no Prizes and you picked Prize, you don't gain anything, as previously discussed. That doesn't mean you can say "I gain followers" and then fail and then not get a different Prize if available - you still have to execute "gain a Prize" if you picked that option and there are prizes available.
Consider a hypothetical Workshop that read "Name a card costing up to $4. Gain that card." In this case, you COULD name Estate, and then attempt to and fail to gain it due to an empty pile. Is it clear why that is? I think so - you are doing as much as the card says, there is no conditional on the first statement, etc.