This is an old thread but it's still highly ranked on Google so I just wanted to chime in that I went down the WinForms path for about a year and I really regretted it. I would highly recommend that everyone go down the WPF route.
For one, WinForms often have some serious and practically unsolvable scaling issues on high resolution monitors. You can read some more discussion here, and while Inter-Process Communication (IPC) is a good option for fixing this user's existing code base, implementing IPC is way more work than just using WPF to begin with, since WPF apps don't have scaling issues.
Additionally WPF UIs are built in a much more modern way, with XML layout documents, separate style documents, and separate code / logic documents. This is much more similar to how UIs are built on other frameworks (like Android / iOS / macOS / web development) and will better prepare you for expanding your development knowledge. This separation also tends to produce much cleaner, more flexible, and more reuseable code.
And lastly, because WPF is a more modern framework, I find that it's just far easier to produce apps that actually look good, and that my users actually enjoy opening up. As developers it's easy to focus on the back end data, but if you want to make a tool that people actually use, it needs to have a pleasing UI, and the styling / dynamic binding nature of WPF makes it far far far easier to produce at least halfway modern UXs.