Look purely st the eyes...
MS
1. Amaterasu: Endless burning black fire
2. Tsukiyomi: Genjutsu that's painful
3. Susanoo: Chakra armor entity that fights
4. Tracking movement
5. Kotoamatsukami: Genjutsu of absolute control.
6. Kamui: Access to an alternate dimension
Cost: Loss of eye sight from continued use. Strong enough to where Sasuke could lose his within maybe an hour of starting combat at the Summit and then against Danzo.
Rinnegan
1. Asura Path: Missiles, swords, Laser things, armor
2. Shinra Tensei: repel anything
3. Chibaku Tensei: Attraction force that pulls everything in an area towards it. Strong enough to require KCM Rasenshuriken, the TBB, and the Yasaka no Magatama to destroy.
4. Bansho Tennin: ability to pull anything or person towards you.
5. Summons: Panda, Chameleon, Cerberus, Bird, Rhino, Crab, etc.
6. Preta Absorption of ninjutsu and chakra. Limited Senjutsu as well.
7. Ability to tear away the souls of people in contact.
8. Ability to resurrect or take life via Hell Gate thing.
9. Chakra rods that restrain movement. Brings corpses to life and with Rinnegan.
10. Linked vision: Paths, Gate, Animals all see the same vision.
11. In unison with Juubi Jinjuriki state: Use of Black KKG that surpasses even Jinton (four elements).
12. Technically as an evolved Sharingan, would have access to previously held abilities (debatable).
13. While resurrected bodies can use one path, the main user holds all abilities to higher and faster levels.
Cost: nothing
Rinnegan #'s 6 and 2 counter Sharingan #'s 1, 3, and 6 if ranged Kamui is used
Rinnegan #'s 10, 7, 8, and technically 6 counters Sharingan #s 6 contact, 5, and 2.
Rinnegan > MS
Rinnegan > EMS only difference is there's Perfect Susanoo and no chakra cost.