The verdict
For a small business that sends a few contracts, I'd pick neither as a first choice. A lighter tool such as Dropbox Sign, or a proposal tool such as PandaDoc, is easier to run. If you must choose between these two, I'd pick Acrobat Sign when your team already pays for Acrobat and lives in Microsoft 365, since the signing comes with it. I'd pick Docusign when the CRM or ERP should drive the contract, or when the field is regulated.
I used Docusign with two previous clients a few years ago. The integrations were the best part, and plan limits on documents and recipients were the surprise. Check current limits before you buy.