There's a slightly simpler solution if you don't care whether the odd ball is lighter or heavier:

It's:

X. AAAA vs BBBB

If X was balanced, XX: C1 vs C2, then XXX: C2 vs C3 (general way to distinguish 2 unknowns: weigh one unknown against one known)

If X was unbalanced, WLOG assume A was heavier. XY: A1 A2 B1 vs A3 A4 B2

Then if XY balanced, use the general method to distinguish B3 or B4 as answer.

If XY unbalanced, WLOG assume A1 or A2 is heavy, or B2 is light, so XYY A1 vs A2 finds the heavy one or implies B2 is light.