Things I think are advantages:
* Unbelievable focus.
I can focus on my work so much that I lose track of time, forget to eat and sleep, and don't even notice other people. This lets me get a lot of work done.
* Perfectionism.
If something is not done to a high quality, that seems like a problem, and I have an urge to fix it.
* An open mind.
If someone told me that the sky was green (and they seemed serious), I would check. If the emptiness above is now a brilliant emerald, then they are right. That's all. I would of course like to know why, but there's no need to panic and no point in denying it.
* Curiosity
I like to know how and why things work, and what's over that fence, and what's behind the locked doors. I want to learn to pick locks just so I can open random doors.
* An ability to make intuitive leaps.
With some math/algebra/calculus/geometry problems, I just write the problem down and look at it. I can usually see the steps to follow to solve the problem in a few seconds, or even the answer to the problem itself. I always have trouble showing my working. Sometimes I don't have any, or don't know what it is, despite knowing the answer.
Now, aspergers is not a requirement for these traits. These are just qualities that I've noticed in myself and other aspies, that not many NT people have. I think that the advantages of aspergers more than make up for the disadvantages, but the disadvantages can cause difficulties sometimes.
Then again, every aspies has aspergers in a different way to all the rest.