The difference will be COMPLETELY different, depending on what type of game it is. Games that are very CPU intensive are obviously going to see much larger increases in performance going from the 1600 to the 3600. Games that are mostly GPU bound will see MUCH smaller changes. There are some games in some of the comparisons I looked at that had less than a 10% difference. Obviously those are games where the CPU is not the limiting factor. In games where the 1600 IS the limiting factor, the increases are going to be much larger.
But it is also worth keeping in mind that most of these gaming and performance related reviews are not done on somebody's daily driver, real world type system. They are done on machines with the bare essentials required to run the testing and produce the results on. For systems where people are potentially running a higher degree of background processes from installed applications, do not have any of the many windows services disabled because they are not needed on a test machine, are not also streaming, or browsing, or recording, or any of a variety of other tasks, then there could be some additional gains in performance there where normally a faster CPU might not show much in the way of performance increase but does because it is more easily able to handle those additional background or multitasking processes.
In other words, lab machine versus YOUR machine, does not usually or necessarily result in the same type of results.