I ran this benchmark for react-native with both bluebird and promise to compare the two.
I think it's worth noting that the margin for error on this benchmark is significant. I do not attempt to claim that Promise is actually faster than Bluebird, but I do claim that the gap between them is small enough to make performance an irrelevant consideration when deciding which one to use.
Bluebird summary:
#ofRuns: 100
Average: 2501.6 ms
Median: 2354.5 ms
Minimum: 2237 ms
Maximum: 3968 ms
StdDev: 362.9 ms
Promise summary:
#ofRuns: 100
Average: 2434.4 ms
Median: 2398 ms
Minimum: 2309 ms
Maximum: 3144 ms
StdDev: 137.7 ms