Since you're new here...I'll give you an answer before this thread is closed...these posts belong in Draft, Keeper, Trade etc. since you're asking who to get of the two.
I'd take Dustin Hermanson, simply because he's shown that he's a better pitcher. He's been effective out of the pen since late last year, even though Hermy was just an average starter. Burgos' Royals don't generate many save opps (even though the myth of better team=more saves is a myth, the Royals just don't get it done) and Burgos was prematurely rushed to the bigs this year. His command is very shaky and thus he'll implode here or there. Hermanson may not be the closer for the entire year and he may not even be the closer right now because Ozzie's doing hell knows what, but he's definitely the better pickup.
Edit: Guru, it appears like Hermanson SHOULD be the closer, at least for now, after last night.