[Freak_NL]

There is a crucial difference here. With FIDO U2F I am not limited to Yubico's offerings; there are other vendors. FIDO U2F devices can be manufactured by any company (and are).

I agree that the ideal situation would be a device that is completely under the control of the user, but compared to IOS or Android, a hardware token that only does what it is supposed to do (in the case of the U2F tokens; register and sign authentication requests), and cannot be modified by the manufacturer after sale is very much preferable.

[superuser2]

That's not a difference. You are also free to choose among many different smartphone manufacturers and OSes, all of which are capable of running a TOTP app.