Change the counter sprocket or rear sprocket?

I am looking to lower my gearing. What is the difference between going down to a 13-tooth counter sprocket or up to a 52-tooth rear sprocket? With the smaller counter sprocket will the engine rev higher or faster? It would seem the counter sprocket might be the better way. I will lengthen or shorten the chain depending on which way to go so the wheel stays in the same place.

I could be wrong, "I was wrong ONCE before"- terrible feeling! Anyway, I believe that 1 tooth on the counter sprocket is equivalent to 6 teeth on the rear!

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