For A516 Gr 70 VS A36, actually they have much difference. A36 plate is typical carbon steel for use in riveted, bolted, or welded construction of bridges and buildings, and for general structural purposes.
A36 plate can also be used in nonpressure parts of pressure vessels such as saddles, supports, etc. But in no way to use A36 plate in pressure parts of pressure vessels such shells, heads, etc. While A516 Gr 70 steel is a good choice in this aspect.
Though A516 Gr 70 steel is also called carbon steel sometimes, it is more special pressure vessel steel. A516 Gr 70 steel is mainly used in the fabrication of pressure vessel containers, suitable for moderate or low temperature service conditions.