The verdict
For a small team that wants its tools to talk to each other, pick Zapier. It is the quickest to learn, the free plan lets you try it, and the app you need is usually there. If your main process is generating, signing and filing agreements, pick airSlate.
The two can sit side by side. A signed agreement in one place can trigger a task in another. I would start with Zapier unless documents are clearly the heart of your operations.