What extension are you referring to, there's a few layered nav. extensions?
I think you can safely say that with every extension you add to your store, its un-cached performance will decline.
Layered navigation on a Magento store is heavy, and arguable one of the hardest to calculate elements on the whole store. Whether an extension makes it slower or not would purely depend on what that extension is doing.
If it adds additional model/collection loads, or extra computation/manipulation of the existing dataset - then it is almost guaranteed to increase page load time.
Ultimately, how the template renders this information out is going to drive whether the performance difference is vast or not.
Let your own testing be the judge of what does and doesn't change performance. Given every Magento store is templated to an individual design - you aren't going to find another store that's comparable to your own.
So you might find some store owners saw an improvement after changing the layered nav, and some may have seen a decline - but you can't really compare apples to oranges.