Hardly 'competing', more like (say) Commodore-64 demo Vs nVidia GPU demo scenes - you pick your arena and push what can be done with constraints (axioms).

In mathematics you might compare groups that work with Vs without the Axiom of Choice, you can can have one group satisfied by an existence proof that asserts X exists otherwise a contradiction must exist and another group that only accept existence proofs that demonstrate a means to construct an example of X.

The habeas corpus divide :-)