Blockchain has an automatic deduction for the miners fee and they are forcing people to pay that "recommended fee". So for me the best online wallet is xapo, it's totally free if you got higher transaction.
So does coinbase. They all pay for the fees as they join the inputs and outputs of their customer's transactions and they send it out so they can all share fees. That is what they do. But the main problem with these wallets are that they are online wallets that require you to submit into their terms and conditions. Which may include that they can unilaterally close your account, suspend it, freeze your account, etc. Another issue, which I experienced lately, was that the online wallet failed! They had a system problem and that my deposit did not credit to my account even after 10 confirmations.