Since I know, I've been using bitcoin some web wallet such as xapo, coinbase, blockchain, green address and so on, after trying a lot of wallets I choose coinbase and xapo because I think better than others.
Yeah, this wallets are good if you're just storing only small funds there and since this wallets are centralized and they keep on asking of user's personal information especially coinbase, well I'm not recommending this wallets anf since you as ther user can't access your own wallet address and that's the worst part of this web wallets I mean accounts.
Normal Xapo and Coinbase accounts don't give users access to private keys and transaction fees, whereas both GreenAddress & Blockchain.info let you choose transaction fee and have access to private keys.
If you are using Coinbase or other trading integrated wallets *only* for storing Bitcoin, you don't have to share your personal information. In most exchanges, you only need to share personal information if you trade above their basic limit.
