For me, it's all about personality. The reason I don't care about the characters in Fate/Zero or Madoka Magica (sorry Triple_R) is because I didn't like their personalities so their stories didn't impact me at all. Okay, the Madoka Magica ones did, but mostly because of the animation. As for what I define as identifiable when it comes to personality? Voice-acting is important, of course. But the most important thing is that the character has emotions and the show is good at presenting them. Can't really say any more than that.
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