What are the limitations of Puppet in comparison to Ansible?
There are of course several pro and cons for each of Puppet, Ansible, Chef and add your favorite tool here as well. So I'll try to stay away from opinion, and share what is great in Ansible as a matter of fact.

The main capability that puts Ansible above the others is not having to rely on some custom/additional agent running on the target nodes, instead being founded on ssh connections only. Yes, it still requires an ssh server, Python and a bunch of Python libraries on the nodes, and if your distro of choice (or, good luck, there are some windows nodes) does not ship with them, it will be a little bit painful to bootstrap. But that's unlikely, and may well even make you think again about your distro.

That will simplify monitoring, not eat additional resources, not force the system to run a daemon as root all the time, and in general feels better inside the UNIX philosophy. Chef has chef-solo, Puppet can be run master-less, but they both work "the other direction," by cloning and via hooks respectively. While with Ansible, a merge in the source repository can trigger the deployment in a fashion we all are comfortable with, be it in Jenkins, in the git master, or in some other tool like Rundeck for instance.