Assuming your New Balance friendly doctor recommended orthotics WITH a stability shoe and now you want Nike or Asics.
So I will say this. Though the structure triax is classified as a stability shoe, I am willing to bet that the Asics Cumulus (their neutral shoe) is nearly as stable as the structure. Nike shoes have a lot of blown rubber in their shoes and it causes them to break down 50 - 100 miles sooner for some people.
I'd vote Asics 2000 series for stability. Also, the general width and depth of the Asics shoes make them more orthotic friendly. To echo the previous poster's suggestion, stability in the Asics shoe might be sufficient by itself. Save the orthotics for your dress shoes and such.