I'm neutral and had Asics Cumulus series from 11 to 13 and found them very good but now the last 3 pairs I've bought are adidas Supernova Glide series.
I've found the adidas runners lighter with less cushioning so it took a while to adapt from the Asics which now feel too soft.
I did accidently buy a pair of Adidas Supernova 'Sequence' which are structured and support, as a neutral runner these were no good, felt awful and gave me real problems. So I would advise you to avoid these..
Hope this helps..