Hi,
I say it depends:
If you just see the current, then it can handle the same as the mosfet.. at least for a short time.
How long .. depends on the power dissipation. If we speak about the same current, then dissipated power depends on voltage drop.
Often the voltage drop across the diode is higher than across DS of the mosfet, then the maximum DC current across the diode will be smaller than the DC current across the mosfet.
If you use external schottky diodes, then the internal diode usually never becomes conductive and thus disspates no power.
Klaus