Personally, I'd got the third party route. It's going to be a lot easier. However, yeah, there are tools. First, get PerfMon. Capture the appropriate counters there. You can program a script, or use the GUI and then retrieve a script, so that you're capturing the same metrics on both platforms. Get that data into a database and then you can run queries against it to compare the two result sets. Next, get Extended Events. You can capture the query behaviors the same way. Again, these can be easily scripted. Output them to a file, then import that into tables. Run queries to do the comparison.
Now, if you want specific counters to capture, that's a gigantic discussion. Four chapters of my query tuning book, linked below, are dedicated to the correct counters to understand disk, memory, CPU, I/O and query performance. Go there for the details.
Or, look to a 3rd party tool that has already done this massive amount of work. It'll be a lot easier. Plus you get ongoing monitoring, historical tracking, alerting, and all the rest of the stuff that you should already have set up on your server.