Do all these 3 applications work same? I mean, if any site proposes to use 2FA and prompts you to use Google Authentificator, can you use other 2 instead?
Yes and yes. The method for turning the shared secret (the QR code you scan when you first set up 2FA on a new site) in to the 6 digit code is universal across all 2FA apps. Any app will work.
I would also give my vouch for Aegis. It is the best 2FA app available at present.
Thanks for the answer, I will take a closer look on Aegis, Authy and andOTP. Never liked Google app, really.