What are the benefits and drawbacks of letting my baby "cry it out? "

First... ...You have to know the difference (individual for your baby) between crying in distress and crying for entertainment. If the latter, all you are doing by responding is making the child more tired and more cranky -- and, like the gambler in the kenny rogers song, "too tired to sleep." this is only the first instance when "want" and "need" are opposite. Wait till they discover chocolate!
Better sleep. The main downside is the trauma that you will experience as your child is crying! there is no evidence that this results in any long term emotional damage to your child. Learning how to fall asleep on their own will serve them well. This seldom takes more than a few days. I recommend a) moving bedtime later by 1 h temporarily to ensure the baby is tired b) avoiding late pm naps.