The main reason why I wouldn't use Google authenticator or Authy is because it's not open source. There's open source alternatives which have been mentioned above which are simply better. Before you say Google authenticator is open source, the app which you download on the store is not.
There's a very good reason why authenticator apps are not open source. You don't want someone to figure out or reverse engineer the algorithms they use to generate the codes.
RSA has been doing 2FA for a very long time. They are considered bulletproof in the enterprise market... they don't publish their code either... for the same reason.
You are more likely to get your account hacked on an exchange where they can turn off 2FA or convince support to reset it for the hacker's 2FA authenticator app.