Of all the tools, I first heard of Puppet first and so I'm assuming it was first on scene? From my limited experience, it seems Puppet is most widely used tool because of that reason. Not necessarily the best of the bunch, but first on the scene. Considering the effort required to roll it out, I am assuming whatever is deployed first will stay as the tool of choice.
I've tried out Puppet, SaltStack, and Ansible, in that order.
What I didn't like about Puppet is that once you deploy a change, the actual change can happen on the "client servers" at any point within next 20 minutes. I may be off on the exact duration but I remember that changes were deployed at any point within that range of time. To me that sounds like not a great idea. What if you want to switch over your web servers at a specific moment? And Puppet requires a dedicated command/control server.
Next I tried SaltStack. I liked it enough. Now that I think about it and hear someone else mention it, yah SaltStack is similar to Ansible. What drove me away from SaltStack was that you essentially need a dedicated command/control server from where all SaltStack commands are sent out to SaltStack "client servers". I did not want to dedicate resource (and money) for a server that is rarely used. And the personal web/lab servers I manage can grow small/large from 2 servers to 10 servers.
Next I tried Ansible. I think Ansible is the perfect choice for me. I only needed to 'devop' just a handful servers and also learn a tool that many businesses seemed to want on resume. So I picked Ansible and it's been great. Some operations are not as flexible as doing it with a shell script (and I assume same issue exists for other tools). But I've had good luck combining Ansible with little bits of shell script to get the result I need.
The best part of Ansible is that any Mac or Linux machine can be used as the "command server", provided that you have the SSH key pair on your Mac or Linux machine.
Lastly, some may not like the ad-hoc way of doing things on Ansible, but I prefer it that way.