Have you enabled Query Store? If not. do that in both environments. Then run your tests and collect the information to compare performance of the queries in same environments. Pay particular attention to Reads. From what you say, we can expect Duration to be widely different. But if it is only a matter of the two environments being different as such, the number of reads would be the same.
On the other hand, if the number Reads is a lot higher on the Linux box, I am inclined to think that it is an issue with query plans being different, rather that different performance as such of the environments.
Of course, I am here assuming that you really the databases in the two environments are copies of each other. If they are not, that alone can explain the difference.