Very tempting to include a familiar face-off here, but as this is for non Alien/Pred chat, I'll omit it. Choose your favourite from each.
1. Sega vs Nintendo?
2. Sony vs Microsoft?
3. Console vs PC?
4. Deep Impact vs Armageddon?
5. Finding Nemo vs Shark Tale?
6. The Prestige vs The Illusionist?
7. Playstation 1 vs N64?
8. Mario vs Sonic?
9. Sunshine vs Interstellar?
10. Batman vs Iron Man?
11. Coke vs Pepsi?
12. McDonalds vs Burger King?
13. Android vs Apple OS?
14. PC vs Mac?
15. Facebook vs Twitter?
16. Bacon vs Cheese?
17. Left wing vs Right wing?
18. Science vs Spirituality?
19. Reebok vs Nike?
20. Family Guy vs The Simpsons?
21. Marvel vs DC?
22. Mortal Kombat vs Street Fighter?
23. Cats vs Dogs?
If you can think of any more rivalries then suggest them.