If you like Rei, you must hate Asuka and vice versa - if you're a fan of Asuka, you must hate the little windup doll. That seems to be the general attitude of Evangelion fans - on the Net, anyway.
Now why is that? I've been thinking it over and the answer's quite simple: the two ladies are like east and west, fire and water. The difference is what attracts different people. What one finds adorable in Asuka one finds deplorably lacking in Rei, and what is charming in Rei is almost nonexistent in Asuka.
Rei is silent, almost conspicuously so. She does what she's told without asking questions, which includes piloting Eva. Never will she retreat unless she's badly injured or ordered to. An exception to this rule occurs when Shinji's Eva 01 is swallowed by the Sea of Dirac, when at first she disobeys Misato's direct order to retreat. The point is, Rei is to those who hate her no more than an automaton, a pretty decoration.
And yet she is touching in her wordless way. Because she lives to pilot Eva (and for some other purposes, okay, okay) she doesn't even realize the joys of communicating and connecting to people (Shinji has his own perspective about this, but that's neither here nor there). Before she learns to feel, she has to want to feel first. Her emotional development is painstakingly slow, and she has to achieve it with scant help.
Fraulein Souryu is another matter altogether. Brash, eager and highly self-opinionated, you can say she's everything Rei is not. She can be very annoying at times, disregarding others' feelings or views, and more often than not condescending, disparaging even, toward Rei and Shinji.
But Asuka has had a bitter past (seeing your mother hang from the ceiling can hardly be pleasant for anyone of any age), and she has learned that she is the only one capable of making herself worthy of esteem. She is human in the sense that she can feel pain and either learn from it or get crushed beneath it. Her tough-guy attitude when in the entry plug is also a plus point - for her fans anyway.
So, who is better, Rei or Asuka? It depends on who you are.