0, as far as I know. It's like the difference between A53-B Type S and A106-B. You're buying the same physical thing that's "dual certified."
If you look at the relevant ASTM material spec grade 4710 meets all the requirements of 3608. So all 4710 could be 3608, but not all 3608 can be 4710.
Some manufacturers are still stuck with 3608 type product, but the major players I dealt with all had 4710.