Can you explain what the advantages of the dominant marriages are? Since you mention Islam, I assume you're the dominant one. I'm going to assume your wife is happy in her role. Do you think the female can be the dominant one in a relationship, too, or how is that decided?
The word “dominance” seems to carry a negative connotation in the context of interpersonal relationships. There a lot of historical factors that are the cause of this and it's beyond the scope of this conversation to delve deeply into that.
Nonetheless, as far as Islam is concerned, it is the role of the man to wield the influence/be dominant in his household. This is by virtue of his responsibilities -- his attachment to the Masjid (or “Mosque” in the West), his duty to earn a living for the household and his duty as an educator and paragon of good character, not just in the home but in his community as well.
The word “dominance” may suggest a sense of oppression in modern times. But in the scope of Islam, that husband who is “dominant” in reality eschews all reprehensible conduct that could be associated with the word.
As I mentioned before, yes, in Islam there are expectations on the Muslim wife. But likewise there are expectations (if not more) on the Muslim husband. Again, that Muslim man assumes dominance in the household out of the necessity that is to submit himself both internally and externally to the conduct of the Prophet Muhammad (peace and prayers be upon him).
The advantages of this lie in the husband assuming his natural role as prescribed by Allah and exemplified by the Messenger of Allah (peace and prayers be upon him). If the situation were to be reversed, then this could not be the case. If anything, the man would not just be neglecting his duties as a husband, but as a Muslim as well. If the situation were to be reversed, it would behove the woman to instead leverage this dominance in order to encourage her husband to fulfill the rights he owes to her and to humanity. If he accepts this, then the natural order as described above would inevitably fall into place.
It is strange to assume that two people who are different by their very nature can be “equal”. The sense of equality between a man and a woman can only come about by the fulfillment of the rights that exist between the two of them, which are different but have to be observed reciprocally.
The problem is that we (meaning humanity at large) are totally unaware of the rights that we owe to each other. Not just in the household, but outside of it as well. Worst of all, we are unaware of the rights that are due to our Creator.
May Allah, the One who is Most Gracious, strengthen you and your wife. Ameen.