Actually, I think you can compare them in SOME ways. I saw an old article here explaining how Rapunzel is not a ripoff of Ariel and explaining the differences between the two. That was a good way of comparison. Or how 2 supposedly opposite DPs like Mulan and Aurora actually have some things in common.

It is hard not to pit them against each other, though, since we all have our preferences and dislikes.

In someways you can compare they (Merida and Ariel) and in other ways you can really, (Merida and Aurora)

It's more the mindset behind it which sometimes bothers me sometimes....as if saying that Ariel is not smart automatically means that she is a bad character (she really isn't), and the need to pull certain princesses from the pedestal. There are some people who seem to hate Belle winning anything just because they think that she is overrated, can't stop dissing Aurora's beauty (well, she is considered the most beautiful by many, it is the ONE countdown in which she is always high, can't you give her at least that?).
I think every princess can win at least in one countdown....Show White for example should win if there is ever a "who is the most tolerant" countdown, Ariel will get my vote for "most adventurous" any day and Tiana is the most ambitious of them.

As long as the diffences are understood and accepted, why shouldn't there be comparison? I think it's a good exercise, even for the intelectual value it implies.

^Well, I went over that in my comment. People mostly seem to compare them to as a means to praise one and hate on another.