the benefit of running it locally is you don't need to trust someone else to hold your wallet.
the disadvantage is you need to manage it all yourself, such as keeping up with the block chain, backing up your wallet, etc.
it's just a matter of which tradeoffs matter more to you.
You could use a wallet service for your every day transactions and still keep a local wallet. Transfer your coins from the wallet service to your own harddrive only once in a while if they exceed or fall below a certain threshold. It will take more time to catch up on latest block on the local harddrive if you didn't start bitcoin for a while but at least you can schedule at which time your computer slows down.