Joseph described Maria Elisabeth to Leopold in a letter of 1781 as "merely mad" as opposed to Marianne who, according to him, was "like a harpy", suggesting he at least felt no very warm feelings after Maria Elisabeth had left the court. Derek Beales says both sisters went off to their respective convents unwillingly, strongly encouraged by the emperor (or rather, discouraged from staying in Vienna). Joseph did not appear to wish to have anything to do with them subsequently, not even sending for Maria Elisabeth when he was dying. It's not clear what the archduchesses felt, but as neither were renowned for extreme good nature, it would have been very natural to have resented this unpleasant treatment.
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I wonder why was Maria Elisabeth termed as "mad"? Marianne being "like a harpy" is quite unclear to me as well. I think I've read Marianne could be unkind to the servants in Vienna (like Maria Christina and Maria Carolina) but I'm also unsure if it was due to her ill health (or if such a claim came from a reliable source). It seemed to me that she was happier in Klagenfurt, where she felt loved by the people. She also maintained a stimulating environment there, with her salon, masonic lodge, and continuing her scientific interests. As for Maria Elisabeth, she also seemed happier in Innsbruck -- being the center of attention there, going out (certainly not like a nun) and not being answerable to anyone on a day-to-day basis. I think it's just Joseph disparaging those whom he clearly didn't like.
Incidentally, Maria Elisabeth was not a vain airhead who wasn't interested in anything except her good looks -- she had a very strong interest in music. Not only did she have a lovely voice but she was the most (musically) talented among her siblings. She played the keyboard extremely well and built up a rather impressive collection of music, which was inherited by one of her nephews (a son of Leopold, if I remember it right). Not to mention her artworks (rather good for an amateur).