Other trading platforms are centralized. They have gigantic centralized wallets where they hold all your funds. So your funds can (and probably will, as history shows with MtGox, Bitfinex, Cryptsy, etc.) get stolen or lost.
But EtherDelta is different. EtherDelta is decentralized. When you “deposit” to EtherDelta, you’re sending funds to a smart contract. They’re stored in that smart contract in such a way that you and only you control those funds (and whether you want to trade or withdraw).
This actually explains most of the subtle user experience differences that people complain about. Generally, when you find yourself saying “other trading platforms have better user experience, EtherDelta is the worst!,” there’s a reason for that. And the reason involves design decisions EtherDelta was forced to make in order to be decentralized. But the benefit is huge. You don’t have to trust anyone with your funds when you use this trading platform.