@jimm619
In general:
1. Two rooks can mate without further assistance, a lone queen cannot.
2. Two rooks can double attack something, the queen can only single defend.
3. The side with the queen must try for perpetual check, if there are no mating chances; this depends heavily on the pawn formation.
The following game is illustrative: the Black king (with two rooks) is chased around the board and finally finds shelter from White queen checks in an improbable location. The two rooks eventually mate.
White: Ghost of a Duke, Black: moonbus.
[Event "Challenge"]
[Site "https://www.redhotpawn.com"]
[Date "2018.01.24"]
[EndDate "2018.02.04"]
[Round "?"]
[White "Ghost of a Duke"]
[Black "moonbus"]
[WhiteRating "1726"]
[BlackRating "1935"]
[WhiteElo "1726"]
[BlackElo "1935"]
[Result "0-1"]
[GameId "12568270"]
1. e4 c6 2. d4 d5 3. exd5 cxd5 4. Ng1f3 Ng8f6 5. Nb1c3 Bc8g4 6. h3 Bg4xf3 7. Qd1xf3 e6 8. Bf1b5 Nb8d7 9. O-O a6 10. Bb5xd7 Qd8xd7 11. a3 Bf8d6 12. Bc1f4 Qd7c7 13. Bf4xd6 Qc7xd6 14. Rf1e1 Ra8c8 15. Ra1c1 O-O 16. Re1e2 Qd6b6 17. Nc3d1 Qb6xd4 18. c3 Qd4b6 19. Rc1c2 Nf6e4 20. Re2xe4 dxe4 21. Qf3xe4 e5 22. Nd1e3 f6 23. Ne3d5 Qb6d6 24. Rc2c1 b5 25. Rc1d1 Rf8d8 26. Nd5e3 Qd6xd1 {This seemed like a good opportunity to explore a Q vs 2R ending.} 27. Ne3xd1 Rd8xd1 28. Kg1h2 Rd1d2 29. Qe4b7 Rc8d8 30. Qb7xa6 Rd2xb2 31. Qa6e6 Kg8f8 32. Qe6b6 Rd8d2 33. Qb6c5 Kf8e8 34. Qc5c6 Ke8e7 35. Qc6c7 Ke7e6 36. Qc7c6 Ke6f5 37. Qc6c8 Kf5g5 38. Qc8g4 Kg5h6 39. Qg4h4 Kh6g6 40. Qh4g4 Kg6f7 41. Qg4h5 Kf7e6 42. Qh5e8 Ke6d5 43. Qe8f7 Kd5e4 44. Qf7b7 Ke4d3 45. Qb7xg7 Rd2xf2 46. Qg7xh7 f5 47. Qh7d7 Kd3e3 48. Qd7a7 Ke3f4 {At last, the king finds shelter from checks.} 49. Kh2g1 {This leads to a quick mate. The alternative Qb7, Rxg2+; QxR, RxQ+ etc. gives Black a won pawn ending.} Rf2xg2 50. Kg1f1 Rg2c2 51. Qa7a8 Rc2c1 0-1