the only difference is that they don't give profit on the money you give them (like your bank account does) and also they don't offer things like loans (which banks do). in any other sense they ARE a bank.
and being first and big, gives them that edge too. if they wanted they could become a huge company worth billions of dollars. of course being in US has its restrictions too...
I think it is already the biggest online wallet for bitcoins. Xapo is the second best but it is not as widely used as coinbase. Also previously coinbase transactions were free and there were no tx fee as coinbase paid the fee themselves. Later on when the bitcoin tx fee increased, they are still charging nominal fee from their clients.