Sun conures, which I believe were the birds being chased, reach 35 mph in horizontal flight. Most falcons can match that, and it looked like the raptor chasing the conures, did. Diving and agility are different stories though. A parrot can dive and increase its speed, and are also probably more agile than most falcons. Could’ve been an accipiter, but falcon is more likely given how much effort it put into the chase.