I would say EIE wield much more power and have much greater capacity for dominance than any other type.
They're aristocrats, asking, obstinate, process, Ej, Se valuing, non-Fi valuing, have higher IQ than most other types.
SLE are too error prone and with their Fi PoLR they don't have the capacity for dominance that EIE do. Generally, the SLE is never the dominant one in relationships with their dynamic quadra mates.
I would say ILE-Ti are stronger than SLE because they're smarter, they're better at saying no than SLE, and they don't suffer for it.
SEE aren't very common, they're Fi valuing so they're more willing to help people than EIE are (EIEs don't always realize and admit that they do what they do primarily for themselves), and they're democrats, so they don't have as much capacity for dominance as EIE. And EIE are extraverted Js which makes up for being 2 less dimension Se than SEE.
LSE don't usually get to rule huge portions of the world like EIE do.
ESI-Se are strong and people usually love them, but they aren't power-seeking like EIE and ESI-Se are more concerned with wealth and with their close ones.
I think LSI-Se have good social skills (better then ESI-Fi social skills), but they're too impulsive, don't go along with changes very well, and are not very imaginative (they're pretty by the book or their personal experience when working) so they don't make it into huge leadership positions much. And sometimes when they have a hard exterior that alienates people and makes them unpopular. ESI-Se have more overall power/influence over others than LSI-Se though due to ESI-Se being more flexible, having more charm, not ever rubbing people the wrong way. LSI-Se aren't as good at task switching and their goals are often aggressive, so they usually have to work with smaller associations. So LSI-Se are generally less happy than ESI-Se because LSI-Se generally don't meet their goals as much and they're not as realistic (their sequential thought process based upon experience or theory means they don't have as good of awareness of the present reality as ESI-Se do).
Anyway, I'd say EIE (either subtype), ESI-Se, and ILE-Ti have the most capacity for dominance (but ILE-Ti moreso in private business and dealing with others than in politics; those three types are generally about what they want, they're great at saying no, they generally have vision and foresight, they almost always have high IQs, they rarely make major errors that they can't recover from, they have great social skills, are charming, they multitask well, they have soft exteriors, they're creative, and they usually look beautiful, they usually have strong bodies and very high amount of internal drive/they're energetic, they speak well to audiences, they don't spend much time initiating much one to one conversation, so people want to be their followers). The LIEs and Beta STs are usually too error prone to accumulate much power although Donald Trump is a modern exception, but a lot of it has to do with his brain being hardwired to be narcissistic and histrionic.
But the EIE is still the type that "rules the roost" the most, they crush/run people over more than the ESI-Se and ILE-Ti and they're aristocrats so they demand that others, large numbers of people give them what they want than working for it on their own without help; they usually have to assemble large groups of people. I don't like EIE.