I could never get why Ansible was popular - to me it felt like a real step backwards from Puppet. Running a bunch of commands once is rarely what you want (except perhaps for deployments, but there are dedicated tools for that).
For deployments, for upgrades, for setting up testing/staging machines. We picked it because it's agentless (just seems to self-evidently be better for our scale) and written in Python (the devil we know and love). Ours is a reasonably stable and a fairly small environment (~40-50 hosts, mostly containers), and it has been a very good fit.
Granted, moving from wiki pages and ad-hoc scripts to any system would have been a big improvement.
How so? Ansible describes a sequence of mutative steps, Puppet describes a desired end state; the latter seems far more amenable to immutable infrastructure than the former.
We run ansible-pull as the very last step of a CloudFormation build (instance or autoscaling group). So it's a local pull, not a push from somewhere else. Only done once, hence the immutability. To make changes you replace the instance.
Puppet (can) keep it's hooks into an already running instance and continue making changes to it.
Granted, moving from wiki pages and ad-hoc scripts to any system would have been a big improvement.