They're both pretty short OVAs packed with action and magic.
They incorporate mythology and philosophy with a bit of a twist (the second 3x3 OVA has more of these elements than the first). Unforeseen twists at the end in both shows.
3x3 Eyes has a better fleshed out story, more character investment & action (also gore).
Shamanic Princess has a dreamier, art nouveau-esque style and a greater focus on magic.
There is a romantic core around which both stories evolve. This is a more innocent love in 3x3 Eyes complicated by circumstance and a more mature, grown-up sort of love in Shamanic Princess. There is a bittersweet element to
both shows' romantic arcs. 
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