Does the RPM of case fans make a big cooling difference?

Does the RPM of case fans make a big cooling difference? Thinking whether to get 3000 RPM fans for the case (not only for the CPU cooler). Noise is not a very big consideration, but if the difference in CPU temperature between high and low RPM case fans is only 2 or 3 degrees, I will give them a miss.

From my own comment
The biggest difference is the airflow efficiency - which on most PC cases is absolutely abysmal. There is far too much variable to make this into any kind of yes/no answer.

So, just to be able to post some airflow designs to show how difficult it would be to make an accurate decision.

Poor design…
Random airflow, no coherent flow design, some areas with no flow at all, CPU fans pulling air down towards the motherboard, RAM mounted across the airflow, wires all over the place interfering still further.

Advantages of higher rate fans, debatable. You'd pull more air in & push more air out, but where it would go in the meantime & how much good it would do is a CFD nightmare.

Good design…
3 distinct, unconnected flow paths, all areas with flow, CPU fans pulling air through in a straight line, RAM mounted in the same line as the airflow, no stray wiring at all.

Advantages of higher rate fans, none. They're not needed. The fans in this machine peak at 5000 rpm anyway.

Labels added, for anyone not familiar with this design.