The only drawbacks are price and difficulty of installation and replacement - you have to tear apart the entire rear-end of your bike. The only thing to note is it needs to be kept much tighter than a chain or it will eventually delaminate and fail. The benefits are quieter, smoother power application, low maintenance, cleaner wheel (although it all still gets quite dirty, just not caked on chain oil dirty) and ideally a much longer lifespan than a chain.
Would I do it again? Probably.
