Here is my personal opinion of some Pros and Cons for the types of jobs that are in the fuzzy area of overlapping functionality.
Jenkins gui and interface handles lots of standalone jobs more nicely.
Jenkins has much better support for parameterised jobs that can be kicked off manually.
Airflow can handle dependencies between jobs in a much better way. Nicely defining and visualising dags of job really is the killer feature.
Browsing task/job logs is nicer in Airflow IMO.
Airflow scheduler is flaky - hopefully better in 2.0.
Airflow has much more “magic” than Jenkins this is often infuriating.
All that said, my preference is to move jobs to Airflow. Getting a nice gui for manually triggered jobs in airflow is/was the only large missing piece for me.