Fischer's game below may have been posted, but didn't want to look through 7 pages.
Two coordinated rooks on an open board (not many pawns) and the queen can struggle to keep up. That's in an endgame.
In the early game with many pawns (and minors) still on, it's a good bet the rooks can't get active enough.
But what about in between? In Fischer's game, he has his queen vs two rook in the mid game with some pawns and some minors off. Can the rooks be active enough? The game is instructive.
IMO fischer's 19...c5 is really impressive. The engine doesn't like it at first, but I wonder if after a long thought it would rate it best or near best.
White always has the idea of taking on e6 twice, so first of all of course, 19...c5 is fighting for the e5 square.
Secondly, even if white does take twice on e6, the resulting bishop vs knight endgame is improved with the pawn on c5 instead of c7 I think (simply because it's closer to queening after the king inevitably infiltrates to the queenside).
Of course it helps that the bishop vs knight endgame favors black (king would be closer, and c3 is a weakness). So moves 16, 17, and 18 I think were part of the evaluation when deciding to go for the trade.
Around 1999, Larry Kaufman did a highly praised article in Chess Life Magazine in the USA where he studied 80,000,000 positions and concluded the old Fred Reinfeld numbers were wrong and that Q = 9 3/4 pawns, R = 5, B = N = 3 1/4, P = 1.
So two Rooks are stronger than a Queen ON AVERAGE. Of course it depends on the position: for example, we know rooks are stronger when they are connected.
This question is clearly not easily answered. The same question was asked here in:
2013: https://www.chess.com/forum/view/endgames/is-it-better-to-have-1-queen-or-2-rooks
and
2008: https://www.chess.com/forum/view/general/which-is-generally-stronger-a-queen-or-two-rooks
If there are enough pawns on the board and the side with the two rooks has a king with a safe haven then I would say that the two rooks will prove superior, especially if the side with the rooks can get a protected passed pawn. Remember in order to over load a piece one must have more than one attacking piece when the pieces are protected by a lone king, and having just one queen is not enough to make any kind of threat to the king unless they can "clean up" the position by grabing lose pawns. Usually the side with the queen can "clean up," meaning they give checks and take pawns that are lose because of their mobility, however, if this situation does not exist, where all the pawns can be protected, and the King is out of the way from checks, then the two rooks should prove to be more superior, however, I do not think any ground will be made if a breakthrough to create a passed pawn for the side with the two rooks cannot be made.
I remember a long time ago, when I used to go over possible variations of moves during a daily chess game, and I would get into positions that resembled nothing in game, as usually the opponent would make a better move that I missed and I would lose the game, or my opponent will make a stupid move and I would win the game and avoid the long drawn out position that I was cooking up, and in this case, it was a queen vs two rooks and a bunch of pawns on both sides. In that game, black was able to support a passed pawn which would eventually queen and would win him the game. I would post that game as an example, but I forgot which exact game it was, and remember the ending was hypothetical, my opponent missed his chance to get to this point, and I simply won. So I'd have no idea how to find out which of the many daily games I've played this hypothetical continuation occured in 
. I wish I had saved the position. Oh well, live and learn.
Depends on the position.
Some people will take 2 rooks over a queen, because of material, but I would take the queen because it controls a lot of space. With checkmating purposes, I think 2 rooks would be the shortest, but blocking off territory would be the queen.
But as I said, it depends on the position and what your goal is. Rooks are very good with stalemating, while queens have a very high chance of checkmating.
The only reason why I said stalemating is because I have played a few games were I have played with rooks and I trade them off and within a few moves, it's stalemate. If you play with the queen, then if the king is on the back rank, the the queen can just block the file above/below. But queens can result in stalemate if not played with properly.
So the answer is:
Depending on the position, you could take one or the other with helping you reach your goal. Though, they are both great choices, whichever has the best guarantee of a shorter checkmate.
Which side do you prefer?
Equilibrium
Two Queens vs Queen and Two Rooks
Black to move
White is approximately +1.00 ahead in this starting position
4r3/1p3k2/p4p2/4r2p/5Q2/6P1/PPP2P1K/8 w - - 0 16
It depends on the position. Overall it's the two Rooks. Larry Kaufman did a highly praised study published in the 1990's in Chess Life of 80,000,000 positions where he determined that a Queen is worth 9 3/4 Pawns, a Rook 5, a Bishop 3 1/4, a Knight 3 1/4, a Pawn 1.
Of course Rooks are worth more when connected to each other than not, so, again, it's the position.
Graham Banks from the chess engine community said from his obervations that generally the queen has the edge more often than not.
Forget two rooks, a Queen would have a hard run against two connected knights!
it's depend on opponent king position
"It depends on the position" is true but you have to elaborate further. Safe king usually favour the rooks, and open or airy king favour the queen.
Once again, take a look at post #117.
In a pure ending with symmetrical pawns and no other pieces, 2 rooks win 62-38% of the time.
There are many exceptions, but generally, 2 rooks are better than a lone Q.
yes it depends on position of rooks for sure. also skill level, a queen is easier for novice. i would take the queen and a positional advantage, or the rooks with the same.
Most players would feel comfortable having the queen, since it's easier to use. Of course, it depends on the position.