Generally yes. But the basis of rated current cannot
be assumed identical.
Current rating may or may not track die area, it has
other constraints such as wire bond diameter, number,
package thermals etc. A diode with better Vf@If(max)
can have a higher rated current as its Pdiss will be lower.
Conversely a PN diode with same rated current may then
have a smaller die, and similar series R.
But voltage goes pretty straight to drift region thickness
and doping and area, with that, to resistance (t*rho/A).
PN diodes modulate that downward in high level injection
while Schottkies do not.
Fast recovery diodes may be a superior option but these
often trade conductivity modulation for storage time
reduction (either lifetime-killing implants like Au or Pt,
or distributed "recombination plugs" that getter minority
carriers that stumble into their local repletion region,
or some combination).
A PN rectifier with too-slow recovery will let charge
slosh back out from the load. That's also an efficiency
hit. There's a "sweet spot" involving forward loss,
reverse losses (Qrr and leakage) and the frequency
and duty cycle of all that.