The biggest difference between coinbase and bitcoin-qt is that coinbase is an online wallet, and has all the security vulnerabilities of being something hosted on the internet. That being said, they have pretty aggressive security and I feel confident in keeping small amounts of BTC there. Bitcoin-qt is a wallet that is stored locally, and as such, lacks many of the security vulnerabilities of an internet wallet, but you are totally and entirely responsible for its managment (e.g. if you forget your passphrase for an encrypted wallet there's no way anyone can really help you).

So really it boils down to your security comfort level. If you're comfortable with someone else holding and protecting your asset than coinbase should be fine, if you're concerned about someone else holding your assets and/or you want total control and responsibility, something like bitcoin-qt maybe more for you. Additionally, there are multiple online wallets that exist, and the arguments for and against are all analogous to the coinbase case.