The verdict
This is rarely a real choice. If you run contracts, onboarding packs and approvals, I'd pick airSlate. If you ship software, or you want any agent-written or human-written files to have a reviewable history, I'd pick GitHub.
A small B2B team that writes code with more than one contributor, human or agent, should be on GitHub regardless, and its free plan includes private repositories. A team that only needs the odd signature should skip airSlate and use a lean e-signature tool. Ask for an altaFlow demo before you commit, because the airSlate brand has changed shape and pricing is by quote. Do not use GitHub issues as your planning tool once your roadmap grows.