Two connected rooks are slightly better than a single queen. The advantage lies with the player who has the initiative.
In this game, the White, with the single queen, is the one with the initiative but cannot break through the Black’s defence. White declines a few forced draws along the game, but is never in real danger.
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Na5 6.Bb5+ c6 7.dxc6 bxc6 8.Qf3!? (The Bogolyubov continuation of the Two Knights Defence.) 8…Rb8 9.Bxc6+ Nxc6 10.Qxc6+ Nd7 11.d4 Be7 12.Nf3 (One interesting try is 12.Ne4!? But this lead to a Black victory in Leimkuhler-Heidsiek, corres., 1977/9. The game continued with 12.Ne4 Rb6 13.Qa4 O-O 14.O-O f5 15.Nc5 f4 16.Nxd7 Bxd7 17.Qxa7 Bb5 18.Re1 Bh4 19.c3 Bxf2+ 0-1.) 12…Rb6 13.Qa4 exd4 14.O-O (Tempting is 14.Nxd4. But after 14… Rb4 15.Nc6 Rxa4 16.Nxd8 Bxd8, Black wins a piece. And after 14.Qxd4 O-O 15.O-O Bc5, White’s queen gets kicked around.) 14…O-O 15.a3 Bf6 16.b4 Ba6 17.Re1 Bc4 18.Qxa7 Qc8 19.Bf4 Rb7 20.Qa5 Bb5 21.Bg5 Bxg5 22.Nxg5 Nb8 23.Ne4 Nc6 24.Nd6 Qd7 25.Qxb5 [Surely better is 25.Nxb5 Ra7 (25…d3 26.cxd3 Rxb5 27.Qxb5 Qd4 28.Nd2) 26.Qb6 Rb8 27.Qc5 +-] 25…Rxb5 26.Nxb5 Nxb4 27.Nxd4 Qxd4 28.c3 Qf6 29.axb4 g6 30.Ra2 Rd8 31.Rc2 Qe6 32.Rec1 Qe4 33.Nd2 Qe2 34.Nf1 Qb5 35.Rb2 Qg5 36.Rbb1 f5 37.c4 f4 38.Rc3 Qf5 39.Rbc1 Rb8 40.Rb3 Qg5 41.Rcb1 Qf5 42.c5 g5 43.h3 h5 44.c6 Qb5 45.Rc3 Kf7 46.Rc5 Qd3 47.c7 Rc8 48.Rbc1 g4 49.R1c3 Qb1 50.hxg4 hxg4 51.R5c4 Qf5 52.g3 fxg3 53.Nxg3 Qd5 54.Rc5 Qd1+ 55.Kg2 Qa4 56.b5 Qa8+ 57.Kg1 Ke6 58.Rc6+ Kd7 59.Ne4 Qa1+ 60.Kg2 Qb1 61.Nf6+ Ke7 62.b6 Rh8 63.Rc1 (63.Nd5+ Kf7 64.Rf6+ Kg7) 63…Qf5 64.Ng8+ Rxg8 65.c8=Q Rxc8 66.Rxc8 Qf3+ 67.Kg1 g3 68.R8c7+ Kd6 69.R1c2 gxf2+ 70.Kf1 Qd3+ 71.Kxf2 Qd4+ 72.Kf1 Qxb6
73.R7c3 (Simply 73.Rc6+ draws.) 73…Qb5+ 74.Ke1 Qe5+ 75.Kd1 Qh5+ 76.Re2 [76.Kc1 Qh1+ (76…Qg5+ 77.Kd1 Qg1+ 78.Kd2 Kd5 79.Rc5+ Kd4 80.R5c4+ Kd5 81.Rc5+) 77.Kb2 Qb7+ 78.Kc1] 76…Qh1+ 77.Kc2 Qa1 78.Rd3+ Kc5 79.Rb3 Qa2+ 80.Rb2 Qa4+ 81.Kc1 Qa1+ 82.Kc2 Qa4+ 83.Kd2 Qd4+ 84.Kc1 Qf4+ 85.Kb1 Qf1+ 86.Ka2 Qf7+ 87.Rb3 Qa7+ 88.Kb2 Qg7+ 89.Rc3+ Kb4 90.Re4+ Kb5 91.Rc4 Qe5 92.Rc8 [Again, a simple draw can be found with a check (92.Rc5+ =)] 92…Qe2+ 93.Rc2 Qe5+ 94.Kb1 Qe1+ 95.Kb2 Qe5+ 96.R2c3 Qe2+ 97.Ka3 Qe7+ 98.Ka2 Qe2+ 99.Rc2 (99.Rc5+ is yet another draw.) 99…Qe6+ 100.Kb1 Qe1+ 101.Kb2 Qe5+ 102.R2c3 Qe2+ 103.Kb1 Qe1+ 104.Ka2 Qe2+ 105.Rc2 Qe6+ 106.Kb1 Qe1+ 107.Rc1 Qe4+ 108.R8c2 (Passive, but still enough to draw. 108.R1c2 is better, as White still has a possible check if necessary.) 108…Kb4 109.Ka1 Qd4+ 110.Ka2 Qd5+ 111.Kb1 Qd3 112.Kb2 Qd4+ 113.Ka2 Qd5+ 114.Ka1 Qd4+ 115.Kb1 Qd3 116.Kb2 Qd4+ 117.Kb1 Qd3 118.Kb2 Qd4+ 119.Ka2 Qd5+ 120.Kb1 Qd3 1/2-1/2