How important is CPU cache? When does it become a bottleneck?

Irrelevant. It isn't a valid way to compare anything as the performance difference depends more on the application and implementation. With the Phenom IIs and Athlon IIs tom's did a test to see how much of a difference cache made, in certain circumstances the Athlon's lack of an L3 cache cost it 5-10%, in other cases it made no difference at all.


If you are comparing between families don't even look at the specs, they are not comparable.

Cache can also never become a bottleneck simply by the definition of the word bottleneck. It is still part of the CPU and therefore cannot bottleneck itself, that is just called underperforming.
 

Blandge

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Cache becomes the bottleneck when your data set size is smaller than the size of the cache. This means that the cpu never has to go to system memory to access the information it's processing. Like hunter said, cache performance is important because it defines the performance of a CPU.