The opposite it true, the MCB is slower than a fuse at high current! Generally a fuse pops quicker as the current increases, MCBs steady out as they are mechanical.
As industryspark says though, the calculations should be done for the circuits to ensure the overcurrent protective device correctly protects the cable.
You normally need to ensure protection against overload current and fault current.
An MCB has 2 parts, magnetic and thermal. The thermal part deals with overload current and magnetic part deals with fault current.
The thermal part of an MCB normally has a fusing factor of 1.45. Rewireable fuses have a fusing factor of 2, this means it takes a bit more overload current to disconnect a 30A rewireable fuse than a 32A MCB.
Fault current wise the circuit in either case should rapidly disconnect which is why we need to design them properly and inspect/test them to ensure they comply!
Fuses don't actually blow at their rated current, it takes more, say 8+ amps for a 5 amp fuse. MCB's don't trip at their rated current either, say 8+ amps for a 6 amp MCB. So the 5amp fuse - 6amp MCB is comparable in the amount of current they will need to blow/trip. Same goes for 15/16, 30/32 . . .