Yeah really, I'd argue the latter is worse.
DO order round two... but only if there's chemistry
Date One is like car shopping: the car is pretty and you initially think, "This is it!" But sometimes, the test drive doesn't go as smoothly as planned -- you just aren't feeling it. Similarly, there are times during first dates when the chemistry just isn’t there.
It can be a letdown, but it's more than OK to realize that you're not that into him or her. Contrary to popular belief, you don't owe this person anything -- you promised a first date, and that's it. If your personalities don't mesh, it's better to politely cap the night off instead of ordering additional rounds, sending mixed messages, and using him for free drinks. (Not cool, ladies.)
Here's a rule of thumb: Drink One is customary; Drink Two can be used to feel your date out a bit more; but Drink Three and beyond is reserved for someone you're definitely into.