I would generally not allow adhesive anchors in place of properly installed headed anchor rods. The mechanism of development is different, and the distribution of force in the surrounding concrete will be different. Smooth anchor rods provide very little bond along the length, with the head or nut and washer providing most or all of the resistance. This places the stress deep enough to develop the surrounding longitudinal reinforcement.
A fully bonded adhesive anchor rod will develop as fast as the adhesive and concrete allow, which may mean that it occurs near the surface. Developing into the concrete only assures that the anchor is stuck to the concrete, but tension forces then have to get to the pier reinforcement or the remainder of the footing. This may or may not adversely affect performance in most uses. In order to assure proper connection between anchor rods and pier reinforcement, they should lap sufficiently. Where the anchors are to be pretensioned, I am not sure an adhesive anchor will function correctly.
As an aside, the Big Dig failures were multiple, including use of the wrong adhesive and improper installation. Many adhesives are now specifically rated for overhead and sustained load performance without creep. ACI and CRSI have developed an adhesive anchor installer certification to address the installation failures. During trial testing of experienced installers, most failed the practical exam when large air pockets were found after installed materials were sectioned.