The choice between axe-core and WAVE matters less than people assume. The issues that actually affect users, missing alt text, insufficient contrast, missing form labels, broken keyboard interaction, missing landmarks, surface in both engines. The engines diverge in the long tail: edge cases and recently published WCAG techniques.
The practical recommendation is to pick one engine and trust it day-to-day, then run periodic spot checks with the other on key pages. axe-core has the advantage of being the engine your developer tooling almost certainly already uses. WAVE has the WebAIM brand authority and the AIM Score deliverable, which carry weight in higher education and regulated buyer conversations.
If you're already in the axe-core ecosystem on the build side, picking axe-core for monitoring closes the loop. If you specifically want WebAIM's engine and the AIM Score, Pope Tech is the right call, and we'll cheerfully say so.