There have been many applications of robots for treatment of autism, for example ASK Aldeberan therapy. However, how do the results from these therapies compare to traditional therapies such as Floortime DIR and Hanen - More Than Words?
Robot-assisted therapy doesn't automatically mean that it is separate kind of therapy. You may for example teach an imitation by ABA principles with the robot. In other words, you are following traditional therapies but also using a robot.
Kids may benefit from robot-assisted therapy primarily because robots are usually reinforcement for them, i.e. kids are motivated to interact with them and of course they will learn more. For kids who prefer rules and restrictive environment and behavior, robots are "friendly" because they don't change a lot- they always follow the same program in a same way.
On the other side, it is complicate to do a program for every child individually. Therapist should know how to handle with a robot and a child in a same time and it may be hard. And most important, robot isn't a human so child will probably have more issues with generalization of the skill than (s)he would have with just a human therapist.
Shortly it is hard to give you one answer on this matter because we have different robot-assisted therapies, we have different skills to teach, different children (e.g low/ high functioning autism, or to use proper terminology- different disorders in Autism Spectrum Disorders), etc. If we want to compare benefits of robots then, for example, we should have experimental and control groups, teaching the same skills in the same way with the only difference- presence and absence of a robot.
Some of references:
1) doi: 10.1109/ROBOT.2010.5509327 2) DOI: 10.1075/pc.12.1.03dau 3) doi: 10.1146/annurev-bioeng-071811-150036 4) Pop, C., Petrule, A., Pintea. S., Peca, A., Simut, R., Vanderborght, B., & David, D. (2013). Imitation and social behaviors of children with ASD in interaction with Robonova. A series of single case experiments, Transylvanian Journal of Psychology, 14(1), 71–91. 5) DOI: 10.1007/s10803-012-1645-2 6) doi: 10.1016/j.rasd.2011.05.006