Hello Henrik,
Here is my thoughts, for better or worse . . . Schmidt Trigger is more particular as to threshold voltage as to when it switches, both high and low. TTL switches around 1/2 way between VSS - VDD, if your diodes are different in terms of their switching voltage, as I see it, 1 will work and the other will not, and your VOM might not be high enough impedance to see the difference.
In any event, as I said, those are my thoughts . . .