I will first state that I believe that most, not all, clays have some amount of long term cohesion; i.e. I do not believe that all clays by default have a long term c=0.
That said, for most retaining wall situations, I would use the friction value between the wall and the soil. If I had actual lab testing consisting of drained test results for the soil at the bottom of the wall, then I would use 2/3 of the drained friction angle plus 0.3 or so times the cohesion.
If I had a short term loading condition, then I would just use the adhesion.
My experience with clay soils and retaining structures, indicates that most wall designs are not controlled by base sliding, but are controlled by global stability or overturning. Where it gets ify is when you have a clayey silt kind of soil with a relatively high drained strength. In those cases sliding of the retaining wall can controll and you have to make a judgement on how much, if any, of the adhesion to include.
I would also point out that it is relatively simple to add a shear key to the bottom of footing in clay or silty clays. This pretty much gets rid of the question of how much of the adhesion to use since a good portion of the potential failure plan passes throught the soil and not at the boundry between the materials.