Lets be all honest here. In the wide range world of anime it seems that most directors can nail male characters, however the whole concept of female characters seems to throw alot of directors off. Whenever this is from the source material that they or adapting or just not having a clue there is alot more weaker female character. However when a female character is nailed they are normaly brilliant.
On the topic of the two characters here in Asuna and Mikasa i feel both are not the greatest. Asuna starts of good but then falls into the trap of " i can't do anything without my boyfriend" and just does'nt progress at all. Meanwhile with have Mikasa, the stonecold emotionless female godess. Don't get me wrong she does have potential as the manga is'nt finished (note i know SAO is still carrying on but Asuna gets hardly an screentime in the next books)