My first thought is that banks are already being actively disrupted by cryptocurrency, undermining even new banking startups. Of course, success will be based on whether participation passes critical mass.
My second thought is that established banks (e.g. Wells Fargo) have teams of experienced people doing very boring (but crucial) work around internal and external auditing relating to PCI and other regulations. I’m not saying big banks have perfect privacy and security, but having worked at a health care startup, I know that the startup lifestyle revolves around “do first, go fast, ask questions later,” which inevitably leads to a worse posture for your privacy and money. This is worsened if the new bank startup doesn’t have FDIC insurance, because then you really could lose all your money.
I haven’t researched any particular online bank; this is just general wisdom, and may be wrong.