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What makes you think that a color-switching piece would be weaker than a non-color-switching one?

It is easy to understand that color-boundness is disadvantageous because it means there are squares you cannot reach even with an unlimited number of moves, but color-switching implies no similar disadvantage that I can see.  A knight can famously tour the entire board.

If I were to guess, I would say the Bison is likely weakest of the three, because I conjecture it is more useful to have both a shorter and a longer move than to have two long moves.  The long move gives you speed, but the shorter gives you more maneuverability.  But this is only a guess.