Believe me my rating could say I am 1900 but believe me I have never been able to tell what is better the queen or the 2 rooks.
The answer is really depends on the position
So lets first compare the strengths and weakness of the rooks and the queen
Queen: A queen would is something which would want to eat un defended pawns control a nice long diagonal.
Rooks: A rook is something which would want to control a open file and try to penetrate.
So after these observations I usually follow one very simple rule, the side with the better pawn structure is usually better, or when you have a queen, the more the number of pawns on the board the better, the less the number of pawn’s the better is the rook.
There are many reasons for this. Firstly the queen is a very mobile piece, it will be able to create double or triple threats easily than any other pieces. The rooks are strong when attacking an isolated pawn. This would be a huge advantage when all the minor pieces are exchanged( only if the person playing with the queen has an isolated pawn). One of the most important factors while considering which is better is the pawn structure: the player with the weakest pawn structure is usually the weakest.
Below is a list of how to evaluate the position.
The position of kings. If the side with the two rooks has an exposed king, the queen is usually equal or even superior to the two rooks, since it can easily create threats against the king;
Piece coordination. Two rooks are better than the queen if they are well coordinated. This is very important, as two rooks that can’t manage to help each other will become target of double attacks;
The queen is usually better if there is play on both sides of the board. Since it can reach faster from one square to another, it will be easier to create threats on both wings;
The rooks tend to be more powerful in the endgame. If there are other pieces on the board as well, remember that the rooks cooperate better with bishops, while the queen with knights;
Piece activity. Of course, everything depends on the actual position here, but what we wanted to underline is that, in order for either of the pieces to be good, they need to be, above all, active.
note: All of the above statements are principles not rules, you will get a better idea of how to use these rules when you play these positions out.