I think it delivers a sarcastic look, either way, it just does it differently than the one that actually rolls it's eyes. This one shows more of a contempt, disgruntled, or sarcastic look, so you'd use it when someone says something that is not to your satisfaction. The smiley strikes me as passive agressive, and not angry enough to be anything more.
The one thats smiling and rolling it's eyes (the animated one) shares a similar feeling, but is more lighthearted, in my opinion, or more joking where this one is clearly serious. This one looks more pessimistic and jaded. My point is, I think this smiley is just as useful as the others are, and so doesn't suck, since people aren't always going to be happy, smiling, or joking around. The attempt is to have a smiley for every type of emotion and situation, and the 🙄 smiley has it's proper place.