Escaping deep rough while advancing the ball a long distance requires tremendous club head speed. Unless you are a high-speed player, the odds are in your favor to lay-up in the fairway and attempt to get up and down. Even if you do have speed, we often see many tour players still lay-up out of thick rough when playing in difficult conditions (ie: majors). They know GIR percentages drop when playing out of rough and penalty shot percentage increases. Put ego aside and follow their lead.
It also helps to have the right equipment for the course conditions you play. In thinner grass, a hybrid offers a great option to get the ball out of tricky lies, allowing good height and spin even on these difficult shots. Thicker grass may require a square-faced iron with a thin sole to get the club face on the ball. Loft in this case is your friend- pick a mid or short iron to advance the ball to a lay-up yardage and live to play another shot.