The capture of prisoners was a good source of intelligence. A captured British prisoner revealed that their would be a five day bombardment prior to to the beginning of the Somme Offensive. One objective of nighttime trench raids was the capture of prisoners for the identification of enemy units and for gathering intelligence. Letters and papers carried by soldiers could reveal the situation back home and especially in the case of German prisoners letter from home revealed just how bad the situation in Germany was during the latter years of the war.

As for whether prisoners were a burden, I don't have an answer. I would speculate that Allied prisoners in Germany would have been considering their dire economical predicament but I don't have anything to back that up. Perhaps someone with more knowledge on the area could answer that portion of the question.

Source: Military Operations France and Belgium, 1916 by J. E. Edmonds