I haven't done any scientific tests to measure the performance of Kovenant, so no performance claims. The test package does contain some rudimentary performance measurement runners though. I've run these on a couple different machines and the results varied a lot. So I encourage you to test performance yourself to find out what suits your needs best.
Perf01.kt compares Kovenant Promises configured with standard Java Executor pools versus the Kovenant Promises configures with the default non-blocking Dispatcher. The results I've seen so far is that in general the Kovenant Dispatcher performs slightly better on systems with few CPU cores and out performs the Javas Executors by far on systems with more cores. This is of course what is to expect from non-blocking versus blocking concurrency.
Perf02.kt compares Kovenant Promises versus Javas Futures. The results I've seen so far is that Javas Futures out perform Kovenant Promises on systems where CPUs are few. This sounds logical since on these systems lock contention is less likely and therefor all the CAS loops used by non-blocking algorithms introduce more overhead. But, just like perf01.kt, when more CPU cores are leveraged, Kovenant Promises out performs Java Executors.
Again, I encourage you to measure for yourself. And keep in mind that the number of physical cores in combination with number of threads can have a serious effect on performance. So the results you see on your local machine may differ greatly from the results on a production server.