>Something about predatory nature of both insects seems to tune up their intelligence.
Yep. To be a predator, you need to outwit your prey and think fast, so it's thought to be a natural INT grinder. `w´
Presumably, this could drive up the INT of prey too, but maybe it's cheaper to just be faster/harder to see? But you can't be THAT hard to see, and the speed only saves you in failed ambushes, so planning successful ambushes continues to reward the INT of predators (unless they just enter the speed arms race, like cheetahs or tiger beetles).