Baked versions, even with some oil sprayed on them, tend to be quite hard and dry at times.
I accidentally made some good baked falafel. I rolled the balls, sprayed them lightly with an olive oil spray and (this is the trick, I think, but was not intentional) to transport them to a picnic, put them in a thermos-type container to keep them warm. It seemed to steam them a bit, and soften them (straight from the oven, they would be too hard). They were wonderful! You could do the same with burgers, putting them in a bowl and covering with a plate to let them steam.