I found this wallet and want to test it. I previously used CEX only.
Decentralized crypto exchanges are not regulated by any central authority, whereas centralized exchanges are. So in order words, if you lose your money due a .hack or bad code you can't get your money back. You could be refunded in a centralized system.
Overall in a decentralized system people play by a immutable set of rules, unless enough people agree to change said rules.
In a centralized system, rules can change at any time (transfer rates, fees for dollar to eth conversion, etc ...).
In general I prefer decentralized, but this is more of a centralized vs decentralization issue.
Let me know if any part of my answer was unclear :)