One GFCI at breaker box vs one at each outlet won't make much difference as far as reaction speed goes. Yes, you could probably get a faster reaction by 2 times wire-distance times 75% the speed of light. But frankly this works out to about 800ns per 100 meters of wiring... Not very much difference.
But what might make a difference is the current leakage threshold detectable by an outlet central device vs a panel device. However I haven't convinced myself there is any real difference.
But if you have NO GFCI outlets, installing a GFCI breaker at the panel is a good idea and is potentially a simpler project than replacing a bunch of outlets in say a kitchen or darkroom. Could also be cheaper if you have three or four outlets on the same branch that need GFCI-ing.
All GFCI breakers require that the HOT/NEUTRAL/GROUND configuration be properly wired or they won't work correctly. This is because they detect current greater than a milliamp or two flowing in the ground lead (a bad thing). If you have older residential wiring that does not use a dedicated ground lead or at least use metal conduit (properly configured as ground) then you cannot install a GFCI outlet or breaker without upgrading the wiring.