TheMrZ is right - most of the archetypes exist in the same quantities, but Zealot and Warrior are maybe the most common, and are also the least friendly (other than the Grox, but there's only one empire following that archetype...).
After that, there are the friendly Traders and Diplomats, and slightly less common than Traders (but I'm not sure about Diplomats) seem to be the neutral Shamans and Scientists. Ecologists and Bards seem to be the least common of them all. Wanderers and Knights only exist as your other save games, and act almost exactly the same as Diplomats and Warriors respectively.
Ultimately, there's little difference (if there's actually any), and different regions of space might be more densely packed with empires following a certain archetype than others - for example, somewhere in the galaxy there could be lots of Bards and Traders but few Warriors and no Shamans.
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