This type of dual output CDP is really the only way to discern the differences between the two types.
The differences you are hearing are more to the particular implementation of the tube or ss output stage. Both tube and ss CDPs are all over the place sonically. Difficult to generalize, and the same applies to results obtained with a dual output CDPs.
In a dual output player, it is highly likely, neither output type is fully optimized. I would rather have a designer stick with his opinion what sound good and accomplish his goals good as possible, doesn't matter which design.
Rene