This is a bit of a theoretical exercise but i wonder something about Hamura. If you dislike big texts just read the bolded part and reply, else: thanks for reading it all.
It seems that Hagoromo became Sage of Six Paths because he had a Rinnegan before Hamura had a Tenseigan. The Tenseigan is compared to the rinnegan which seems to be justified. Furthermore, it seems that the Yin and Yang Six Paths powers were used by Hagoromo and Hamura to seal Juubi first and only some point thereafter did Hagoromo drain it's chakra and become it's Jinchuriki.
So the scenario is: What if Hamura had awakened the Tenseigan and taken the burden of the Juubi upon himself, becoming the Sage of Six Paths in stead. Would hamura have the same powers as Hagoromo? Would he get -or give himself- the Rinnegan?. or better put:
If Hagoromo was the Sage of Six Pahts and Juubi Jinchuriki, would he have
- the exact same powers and abilities as Hagoromo?
- would he have the same powers but different abilities (different Path powers)?
- Completely different powers?
Note that when sealing Kaguya, Hagoromo and Hamura had the Yang and Yin Six Paths powers respectively but as Sage of Six paths Hagoromo possessed both. They used Chibaku Tensei to seal Kaguya which is a Deva Path power, suggesting each had half" a Deva path. Note that the Six Paths are divided in Physical and Spiritual powers (Nakara, Animal, Asura and Deva, Human, Preta respectively) too.
Tenseigan is shown to share a Six paths power with Rinnegan(Namely Preta, the ability to drain chakra). So with option 2: Same power but different abilities the Six Paths of Tenseigan would be:
- Deva: Attraction and Repulsion (via Yin/Yang Chibaku Tensei)
- Asura: chakra Cloak
- Human: Glowy Orb People Control
- Animal: Summoning
- Preta: Chakra drain
- Nakara: Golem.
oh and obviously:
- Gedo: Life and Death.
EDIT: added the question of whether he could get the rinnegan