Diode forward current with µV..mV forward bias
Diodes Spice models are usually pretty accurate especially those written by the manufacturer.
The difference lies in how the 2 diodes are designed.
I'm focusing my attention on Is, the saturation current.
It seems to me that the saturation currents Is of the 2 diodes are different.
See this Wikipedia formula which is the Schottky model of diodes:


Is depends, among other factors, on:

The cross-sectional area A of the pn junction

The donor and acceptor densities ND and NA


See this Wikipedia formula:


Happens that the 2 diodes have different cross section and different donors and acceptors densities.