Its more a question of environmental forces than type. Our understanding of personality type is completely dependent on the human culture we grew up in. An INTP human in a primitive culture might look extremely different (though they'd still likely be fairly independent).
If you're looking specifically at domesticated animals there's the issue of selective breeding, which has the potential to wipe out personality diversity, but a successful wild species will likely contain a number of personalities, as that is evolutionarily preferable.
Comparing species is dependent on an us vs. them mentality, lumping an enormously diverse group together based on their dissimilarity with us (i.e. gentiles). For that reason, any thorough approach to comparing the personalities of dogs and cats must arrive at the conclusion that no correlation exists beyond known characteristics (pack-mentality, etc.).
If you want to analyze only domesticated dogs, you might have more success because of how they were bred to be ideal complements to humans, but at best you'll have a comparison too difficult to translate (exponentially harder than the primitive INTP).
That being said, they were bred for human-like traits, and its not overstepping any bounds to apply human characteristic adjectives (i.e. shy, gregarious) to specific breeding lines.
