depth/complexity of decision trees
No, you can't infer that.
I assume you have the same training set with the same predictors (symptoms). The only difference in the training set is the binary class label for each patient.

The smaller tree just means:
- with the given symptoms, it might be easier to distinguish between the people who have the condition 1 and the ones not having it. (since you have the same certainty with fewer information)
This distinction seems harder with medical condition 2, that's way you have to consider more symptoms to be pretty sure about your classification. So if condition 2 is a very mild condition where it is hard to diagnose even for an expert if someone has it then it would result in a deep tree.