In my experience I only had real problems with projects built on outdated frameworks, like cake 1.3, because the framework was not compatible with php7, and upgrading to latest version of framework meant basically a full rewrite.

A few other old sites, even relatively large ones, that were built from scratch or on homegrown CMS years ago, only took some minor fixes and mostly were up and running in couple of hours, some even worked right away without any issues.