Task Master vs Empathetic leader

In my corporate experience, I have observed two kinds of leaders - 1) A hard task master, very high on IQ but more often than not low on EQ and 2) High on EQ, above avg on IQ. I as a manager/ leader fall under 2) and usually get work done without authority but I do experience at times, some peers and reportees taking advantage of my behaviour

In my view, anecdotally I see type 1) leaders succeed more in corporates even if it comes at the cost of facing flak/hate from directs/indirects. One of my previous managers was unpopular for his toxicity but somehow I kind of built a decent bond with him. Once over drinks and dinner, he candidly told me, I'm not here in this organization for making friends and I'm here only to get results and he did deliver on results every year.

My question is, can type 2 leaders even climb up the ladder specially where cut throat competition exists. Sometimes I do feel I need to be more like type 1 leaders obviously not at the cost of toxicity - disrespect, shouting etc.

What are your thoughts?