What is the intensity and depth of Celia and Oliver's love in contrast with Audrey and Touchstone's as seen in Shakespeare's As You Like It?
Celia and Oliver's love certainly does appear to be much deeper and much more legitimate than Audrey and Touchstone's as the former is based more on character. We learn at the beginning of the play that Oliver is the eldest son of Sir Rowland de Boys, a courtier who was greatly loved and admired by the usurped Duke Senior. While Oliver does not at first display his father's characteristics, in fact proving to be quite evil, he undergoes a major transformation once in the Forest of Arden after being rescued from an attacking lioness by his youngest brother Orlando, the same brother he has tried and was trying to kill. Orlando's act of self-sacrifice transformed Oliver into a loving brother who now exudes their father's character traits, and it is likely these character traits that Celia has fallen in love with, showing us that their love for each other is based on character and therefore deep and legitimate.
In contrast, Touchstone is so far above Audrey in education that she really can't understand a word he is saying. He uses twists of logic, saying that he would only want her to be chaste if she was ugly, confusing her so much that she eventually exclaims, "I am not a slut, though I thank the gods I am foul," meaning ugly, which couldn't possibly be true, otherwise Touchstone would not be attracted to her (III.iii.38-39). What's more, she quickly agrees to marry Touchstone, despite the fact she doesn't understand him and despite the fact that she is also being courted by William, who is just as simple as she is. But when Touchstone agrees with Jaques and decides not to be married that instant, Audrey makes no comment, seeming not to be upset, showing us that her feelings for him certainly do not run deep.
More important are Touchstone's professed reasons for wanting to marry Audrey. Touchstone makes it quite apparent that he is doing so simply to satisfy his lust. We especially see him relating marriage to a satisfaction of desires in the lines:
As an ox hath his bow, sir, the horse his curb and the falcon her bells, so man hath his desires; and as pigeons bill, so wedlock would be nibbling. (78-81)
He even has the audacity to whisper to Jaques that he doesn't mind if he is not legally married for that would give him an excuse for later leaving Audrey, showing us just how insincere Touchstone's feelings are for Audrey.