Immediate response, if vibration means ultrasound for you, one advantage of this could be that using a phased array-like system you have at least the potential to concentrate "sensing" on arbitrary locations within your object of observation, whereas FBG means you have the sensor at predefined locations.

Besides, ultrasound as described above would mean your strategy is primarily detection of damage, whereas in an FBG, what you detect is strain and thus the consequence of the load acting on your structure. Damage would have to be inferred from it using some structural & material models that link e.g. strain at the place of measurement to strains in other areas, stress to strain, and then stress or strain to the related expression of damage.

Naturally there is more to add ...

Best regards,

Dirk

You have to divide techniques from sensors.

FBG is a kind of sensor, vibration method is a technique.

There are also distinctions from "damage detection" and "health monitoring".

Furthermore, you can have "local sensing" and "global sensing".

Searching these terms, you can have infinite choices... Depends from your needs.

Basically, vibration method could be a global monitoring, because you measure the structural dynamic response from a pulse solicitation. For this, you can use many kind of sensors, even the FBG, if the FBG interrogator has enough band (minimum 10kHz for some big-defects).