Russ,
Both of those numbers should be used. For motor circuits with high starting currents, you need to know the normal "running" current, probably 10 Amps in this case, but you also need to know the allowable and required size of the breaker or fuse necessary to get the motor from 0 to normal running speed. The US National Electrical Code, Table 430-150, shows that a 3 horsepower, 230 volt, 3-phase motor has a normal full-load current of 9.6 Amps. This is probably your "10 Amp" rating.
NEC Table 430-152 gives the maximum allowable setting of fuses and breakers for motor branch circuits. For AC 3-phase motors, with fuses it is 175% of FLA, and with circuit breakers it is 250% of the motor FLA. However there is an exception to the rule in Article 430-52(c) that allows time-delay duel element fuses as high as 225% of FLA. Assuming your motor has a 10 Amp FLA, then the code allows you to use time-delay fuses as large as 22.5 Amps (probbaly your "25 Amp rating). Your wiring and starter must also be rated for the same level, #12 wire for 20 Amp fuses, #10 for 25 or 30 Amp fuses
The max fuse size is based on using the motor at rated voltage. If it is a 480/240 volt duel winding motor, and you are running it on 208 volts, then it will pull about 10% more current, and the fuse will have to be raised accordingly. I noticed you said it was "fed with 240VAC 3phase". Do you realize how rare it is to have an actual 240 volt 3-phase AC voltage supply? I see a lot of 208 volt 3-phase transformers that are running on the 4th tap, so that you get maybe 218 volts if you are lucky.
If you are using 20 or 25 Amp Class J, K or some other duel-element type on a 3 HP motor, and the voltage actually measures 240 with a meter, and the fuse still blows, then there is a problem with the motor or hydraulic pump.
Because the motor has been moved from a previous location, I would check the voltage first.