There should be a difference in the amount of DNA shared between those who share two grandparents and those who share one grandparent. However, AncestryDNA does not give one the tools to determine this.
You can upload your raw data to gedmatch.com and make the comparison.
Full first cousins will share on average about 1/8th of their DNA:http://www.isogg.org/wiki/Autosomal_DNA_statistics
Half first cousins will be more like second cousins or first cousins once removed.