From my point-of-view it’s more that they seem like two pretty similar clubs - there’s a level of flash that is Spurs-but-not-Arsenal (eg Berbatov), and a level of grit that is Arsenal-but-not-Spurs (eg Tony Adams), but other than that most of their personnel would fit just as well at either club. Pochettino is right in the middle of that Venn Diagram. Mourinho is outside both circles.
I’ve come to the view that a club’s idea of itself is the single most important thing in an appointment. Why Klopp was obviously always our no.1 guy, and why Lampard is perfect for Chelsea - he doesn’t match anything in their past fifteen years, but their fanbase still sees itself as this stylish Osgood-Wilkins-Zola thing despite all evidence to the contrary.