I would like to get some different perspectives on this.
We currently use SharePoint 2013. This was installed about 3 years ago by a vendor. I think it may have been their first install because we have seen several things that were not set up correctly. We have had some weird issues, anomalies and things not working correctly  from time to time. So my thought is rather than upgrade to 2016, we stand up a new farm on new servers for 2016. What are the pro’s and con’s?  What does this involve? Are there any third party tools that we could use to transfer content from  SharePoint 2013 to SharePoint 2016?
Hey Ernie, you’re on the right path. You should definitely build the 2016 farm and migrate there. I don’t see any reason not to.
However, you will want to clean up your old content as much as possible before you migrate, and have a solid plan.
I’d recommend doing an audit of content, then getting rid of things you don’t use. Also, review all your custom applications and features, because they may or may not transfer over well. This is especially important if you started off on an older version of SharePoint, and brought missing references issues to your current farm.
Finally, using a third party tool will make things way easier. Check out that comparison Mark posted. All of them have pros and cons, but they all work too.