We always recommend using API-based integration, unless you run into tracking issues (a high % of leads is not tracked).
API-based integration pros:
Much easier to integrate. cookie-based integration requires updating your website forms, adding new fields, mapping them, etc. It's a whole process.
Cookie-based integration cons:
Currently, cookie-based integration (if integrated correctly) is able to give a higher percentage of tracked leads.
Cookie-based integration supports several fields that the API-based integration currently does not.