You speak of GFCI (I had to google it: it means ground fault circuit interrupter), as if it is equipped with a zero-sequence or differential circuit breaker, protecting against "ground leak"; during my internet search I have found instead "ground fault" mentioned, as if it protects against short circuit, not leaking.
Let's assume that it is like a RCCB in the IEC/CENELEC jargon (RCCB = residual current circuit breaker). It is utmost useful in a range of situations/applications: bathrooms, dish washer, places with humidity (basement, garage), etc. where leaking is quite likely sooner or later, and a person might be in a "disadvantageous resistance situation", that means wet contact, no good isolation, possibly many conductive parts nearby, weak person (not a well equipped worker).
About guarantee of protection compared to traditional circuit breakers (maximum current), it is a bit involved, because standards are traveling at one pace, local regulations at a different one (snail like). In general, when you have TT distribution your short-circuit loop impedance is larger (you are far away from the power source, you rely on local grounding): an RCCB is a must, and it is allowed, or better advised (see e.g. BS 7671 and IEC 60364-4-41).
In TN systems it is not strictly necessary for protection and this is confused with "it is sufficient": it works, it's strongly advisable, but please put a magnetic circuit breaker upstream for short-circuit current.
Nowadays this stuff is not expensive, so again highly advisable.
Cons: there are different types**, sensitive to AC 50/60 Hz (mains), to DC, to -- in addition -- high frequency content. They are thus more complex and need some evaluation beforehand if your application is not a standard dish washer. For complex applications, where you have exigencies of protection and continuity of service (or availability), you should take a look at Residual Current Monitors (ref. std. EN 62020) and Residual Current Circuit Breakers (ref. std. EN 60755, E 62423). Strange applications I work with are: signaling and control implementing safety functions, such as point machine in railways, signals especially in metros (IT systems quite diffused in US and Canada), etc.
**the mentioned types are e.g. B and F, for which the EN 62423 speaks of "with and without integral overcurrent protection". So, the only problem is that they are not a straightforward solution, with one medicine that cures all ills.
Following Transistor's hint, comparing a RCCB in the main switchboard to RCCBs locally deployed at sockets:
- A single RCCB at the main board must be selected/trimmed for a higher leakage current, so less selective.
- A trip will switch off everything (selectivity problem), even when the trip is caused by one specific load such as a conditioner or a fridge with
large dispersion through the cooling serpentine.
- Such RCCB+outlet are not expensive, so they can be deployed at the most troublesome loads, and they will protect just that, with beneficial continuity of service for the rest of the system.
- As said, a local RCCB+outlet can be tailored to a lower leakage current, thus making protection more effective, especially for situations of critical exposure.
- RCCB at outlet is not so different from protecting selectively downstream lines at the main board: the only "con" is that you have to check locally what is the outlet that has tripped, but it's you home or office, not a 10-acre plant (centralized monitoring is a second-order exigency).
All in all, highly advisable, not expensive, and the only caveat is to take care of untimely triggering and suitability for specific applications.