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Minus the Kami Tenchi and Azathoth (How would you even rate them?), the Chousin and higher dimensional beings of Tenchi vs the dieties of Lovecraft.

Who wins?

Lovecraft deities, no doubt.

AFAIK, the Tenchi Muyo Multiverse is something like 22-23 dimensional. The Lovecraft Multiverse is infinite-dimensional, and Yog Sothoth exists beyond the multiverse. This may seem like semantics, but scale matters when comparing characters of this level. Outer Gods > Chousin/Counter-Actor/etc.