You can easily make the converse point and claim that SHA2 has a higher probability to resist future cryptanalysis than SHA3, given that SHA2 has already had a

You can easily make the converse point and claim that SHA2 has a higher probability to resist future cryptanalysis than SHA3, given that SHA2 has already had a lot more research than SHA3, but is still not broken. "Old" is a feature in this sense. The only issue I know about with SHA2 is its length extension property. And that is by design.