You're right about this being a peregrine. The sharp wingtips point towards a falcon, but the wings are too broad-based and short for the other falcon species. It is also a bulky-looking bird, and fairly short-tailed.
In terms of plumage, note that this looks generally pale below (on better views it should be narrowly barred) - Eurasian Hobby should normally appear much more heavily marked with a contrast between the white throat and darker body. If you look closely you can also see the 'moustache' (this is shared with other falcons, of course).
