What is the difference between reactive attachment disorder and asperger's?

Totally different. Reactive attachment disorder is an impairment in the ability of young children to create and maintain a strong bond with caregivers; it arises from a mismatch in child needs and parenting style. Although children with asperger's disorder also have trouble connecting with others, the problem is genetic, with a decreased drive to socially connect plus odd, intense interests.
The care giving. Reactive attachment disorder results when a child's emotional and physical needs are disregarded either through neglect or frequent changes of care giver. A change in care giving with consistency and love brings about a positive change in the child. Asperger's disorder on the other hand is a perversive developmental disorder and not caused by defective care giving.