Compare two servers on SQL query performance
One of the best ways to compare two servers is to repeat tasks that you (hopefully) normally do on both:


Run DBCC CHECKDB
Take Full backups
Run any index or statistics maintenance 


And of course, one of the best ways to measure the impact they have on your server is to look at wait stats. If those pass, then move on to comparing queries. You generally don't want to test query performance in a vacuum, because a whole lot of other stuff may not run the way you expect it to

I wrote a whitepaper for Google earlier this year on how to do this. It's free, and I suggest you give it a read. It walks through how to do all the stuff you're interested in. Even though it's done using Google's Cloud, it's applicable to any server comparison.