The quality of a balanced cable is just as important as unbalanced.
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My suggestion is that before reaching any conclusions you repeat the comparisons without having both the balanced and the unbalanced cables connected at the same time. Before disconnecting or re-connecting any of the cables, of course, turn off the components.
Depending on the design of the two components, especially their internal grounding configurations, it is conceivable to me that the presence of the unbalanced connections could be affecting the sonics that you hear when using the balanced connections, and vice versa.
Also, keep in mind that when you change between the two types of connections you are changing a lot more than the cables. The interface circuits that are being used in both components are being changed, as well as the basic principles upon which the interfaces operate. So I would be hesitant to place too much faith in experiences others may report, unless they were using the same components, or at least similar models from the same manufacturers.