a queen for two rooks?
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A good way to tell aside from the point values is to check endgame statistics and see if historically K-R-R wins over K-Q better than 50% of the time. I would give two rooks slightly better odds of winning so trading my queen for them to avoid that endgame should, hopefully, improve my chances. Always make sure that the exchange doesn't leave you open to checkmate or to a deterioration in your position, though. 1 point of material gain isn't worth losing the game over.
You are overlooking other things in this game. You had a better minor piece. You had a safer king. Had either of these not been in effect, the game would not have worked as favorably. Basically, you were winning even before the trade. Queen trade was iliadvised there, and white even chose the wrong move to do it with. Qc3 was better.
He missed another pin, 5. Qc3. It doesn't of course win any pieces (Rb1+ Ka3 Rd8) but it does misplace black rooks, greatly reducing their effectiveness by hindering their doubling.
10. Nxb5 no, he should not take the knight. He in fact should not be taking anything, but instead playing Nd1!
12. Nf4 doesn't work either. 12. Nf4 b4+!13. Ka4 Rxa2+ (13. Kxb4 Rd4+)
15. Qb8+ He wants the pawn, and rightfully so. Possible checkmate was threatened.
18. f3?? Did him in. Qc6 would of been my move of choice here, as well as on move 19. This move offers still some drawing chances.