Definitely API is the more reliable and robust method of sending events into PagerDuty and can be coded to retry on failure. It also allows for the setting of various payload variables which can then be used in PagerDuty Event Rules and also displayed in the Incidents.

Email on the other hand is basically “fire and forget” and therefore cannot be relied upon. It would need to be sent from a physical mailbox, so at least it could be checked for any bounced emails. You may also encounter issues if your organisation has any throttling rules on their email servers, which could impact the delivery of your email events. With Emailed event payloads, you basically only have the contents of the Email Subject and Body to work with and may need some complex RegEx in order to set a dedup_key.

Having said all of that, in my experience email is much easier to set up, as there is no requirement for coding the sending of an API command. However, once the solution has been written once it can be re-used for other applications with some minor tweaking.