Email Authentication sends you an email to the address of your account. Recently Cipsoft has had technical problems sending this emails, but disregarding this issues it's still the worse option. Anyone trying to access your account will already have your email and if they have access to your Tibia password, it is just one step closer to also having your email password. Thus, it is easier for a hacker to finally access your account.
The main benefit is that it doesn't require you to have a recovery key which right now costs 5.45€ or 6.41$.
Authenticator App requires you to have access to a mobile device, usually your phone with an authenticator app installed in it (or them, since you can have it on multiple devices), or your computer. Having it on your computer is also a security risk since it is where you play Tibia.
It does require you to have a recovery key for your account though.
So all in all:
| Email Authentication | Authenticator App |
Pros | - Convenient access from your computer.
- Doesn't require recovery key to set up.
| - Safest option.
- Can link multiple devices.
|
Cons | - Easier for a hacker to gain access to your Tibia Account.
| - Requires access to your phone or mobile device.
- You must have a recovery key.
|
A recovery key can take weeks to reach your home so Email Authentication is also the best option for a fast setup while you wait for it.
Source: Tibia FAQ - Linking an Authenticator to an Account