His eye is the combination of the Sharingan & Rinnegan, hence having both their design.
Here’s my explanation on why he awakened the Tomoe Rinnegan.
The Original eye is the Rinne-Sharingan, which Kaguya had. The Sage inherited a portion of her power, including the Rinnegan, a watered down version of the Rinne-Sharingan.
Indra & his decendants inherited half the Sage’s power – his Yin side (spiritual energy) , powerful chakra, & eyes powers, the Sharingan, an even more watered down version of the Rinne-Sharingan.
The Sage gave Sasuke half his power – his Yin chakra. It was basically adding the Sage’s Power (Rinnegan) onto Indra’s (Sharingan) which formed the Six Tomoe Rinnegan.
The reason why he only has it in one eye is because the eye itself never existed as a pair. The original owner only had one, so ofcourse a variant would.
Naruto & Sasuke are equal in power. He needed the Bijuus chakra to over power Naruto, which he did til the Kyuubi gave him all the Natural energy aboveground. Nature energy is combined with the users chakra to create Senjutsu which further powers them up.
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Once Naruto gain this boost he matched Sasuke again, hence Indra's Arrow matching the Double RasenShuriken.
If Sasuke was going all out beforehand, & then decided to use the Bijuus chakra then you would have a point, but he didn't even break a sweat.