I would take two Rooks over a Queen most of the time. Of course, it depends on the position. The simplest reason for this decision is because most player under 1700 depend on the Queen far too much. Because of the Queen's broad range of potential position, many players hesitate to trade Queens. Trading Queens works for me because I try to force the exchange to reduce the pressure on my position. I would also rather have two strong pieces than one. Again, it really depends on the position. My chess coach taught me to not rely on my Queen as much as I did and it has changed my game for the better. I am curious what other people think about this subject. Thanks for posting a great question.
As a side note, I teach chess for a living, both in the public and private school system as well as privately. Most of my students will hang on to their Queen because of the notion that the Queen is too valuable to trade off.
And why?