Regarding stopping power
.177 has 16mm2 crossection a .25 has double i.e 32mm2 so what do you think which will cause more damage on a shallow target? A .25 will not drill holes in metal or roofing sheets if there is a pass through, alright maybe if you want to shoot through some chicken wires, with a .177 it is going to be lower probability of clipping. Or with night vision when you have to but can’t range properly the .177 is easier a better choice
Both must hurt when you shoot yourself with, can’t make a comparison but the muzzle energy is the same, at least at the muzzle first. Later the .177 is losing big time energy at 40yards the .177 is close to 7fpe while the .25 is still around 8fpe.