The human mind/brain treats all modalities in an equal way, given modality specific constraints.There are two parts to this Principle. The first part (in the first clause) is the idea that the mind/brain has general cognitive principles that all factor into different domains in similar ways. We should therefore expect that the cognition of spoken language, sign language, and visual language be similar, just as we might expect facets of actions, music, dance, and others to share parts of that same cognitive orientation.
Among the things that might be similar across domains might be: 1) the ability to store systematic parts into our long term memory (i.e., a "lexicon"), 2) the ability to manipulate those parts to make larger units, 3) the hierarchical organization of sequences that enables those parts to be organized in an infinite number of ways, etc.
The second part of this Principle (the second clause) wards off an overextension of these similarities. In some ways, we should absolutely expect that different human behaviors are processed differently. However, we would expect that the nature of those differences is a direct result of the nature of the behavior itself.
For example, we might expect spoken language to differ from drawings in certain ways, because drawings are analog and spatial, while spoken language is digital and temporally constrained. All of these differences are directly related to the fact that drawings are visual-graphic while spoken language is verbal-auditory. The differences come directly from the nature of the expressions.
Overall, this Principle is affirming to the general processes of the mind. Why should the brain create lots of unique diverse ways to handle different behaviors when it can efficiently make use of various general underlying structures (like those listed above) in a variety of capacities?
Coming back to the overall idea of drawings being structured, processed, and learned comparable to language, the Principle of Equivalence demands a counter to any theory going against it. It's notable that this is the vast majority of theories about drawing from the past century, which do not think drawings are structured in a systematic, conventionalized way, but rather that they represent perception.
To these theories, they must address the key question: Why should drawing and sequential images NOT be processed like language or other human behaviors? The same questions should be asked of language and other behaviors: What makes it alone unique and different, and why is that advantageous to cognition or behavior?