I would like to know if it makes sense to migrate this application to Linux
It makes perfect sense.
Apache, MySQL and PHP are "more" native to Linux than they are to Windows, so they may perform better.
What will be the tradeoff or benefits and if we will encounter any technical issues?
Always assume that you'll encounter technical issues.
My advice for you there is, do some research up front to make sure that you have your logging set up correctly, because when the time comes, it will be your only source of information to help you troubleshoot your issues.
Most of the time if you Google what you see in your error logs, there will be somebody online who has dealt with it previously.
You should also do some research into securing your Apache installation, and possibly set up a very basic configuration of SELinux, which will greatly increase your server security.