From a personal perspective, having Aspergers is both a disability and a personality difference.
The disability is my difficulty in understanding social situations as well as a "normal" person. This is similar to culture shock in some ways such as interpreting body language and emotions as well as understanding social rules. For me, body language is a language that is similar to a second language. This may be hard to understand for someone who can easily pick up on non verbal signals but imagine that these non verbal "words" were in a language that you cannot understand. As with a second language, I have learn to interpret non verbal language but I am not exactly fluent in it.
Speaking of second languages, learning Japanese has given me a deeper understanding of social rules by studying another culture and practising dialogue that is similar to a social situation.
One thing that can be both a disability and a personality difference are my semi enhanced senses. There are some things that I can not tolerate sometimes to the point of feeling sick (e.g. the smell of oranges). On the other hand, there are somethings that I find calming such as touching satin.
In terms of personality differences, I find it easier to understand something if it is presented visually rather than verbally. This is common with many Aspies (another way of saying "people with Aspergers"). Because of this, I find reading something easier than listening to the same thing. Perhaps this is why I taught myself to read before starting school.
My visual preference could be one reason why I was drawn to Lolita fashion in the first place. Another reason for this that could relate to my Aspergers is the detail that is present in Lolita clothing.
Speaking of detail, I can be quite detail oriented and sometimes a perfectionist. For example, I can have a very good assignment when marked but I can see it as average.
To end this post, I will quote Simon Baron-Cohen, a renowned Autism researcher in a brief summary of Autism (this can be applied to Aspergers as well).
"Autism is both a disability and a difference. We need to find ways of alleviating the disability while respecting and valuing the difference."