Traditional Mainstream Christians (Protestants and Catholics) tend to insist that in a marriage the wife should "submit" to her husband - that specific word submit is used a lot.
By contrast, Mormons (who are - let's be honest - the experts on marriage and family in the modern world, and who are free-er of the taint of liberalism/ leftism/ feminism than most other Christian denominations) say the following:
By divine design, fathers are to preside over their families in love and righteousness and are responsible to provide the necessities of life and protection for their families.
Mothers are primarily responsible for the nurture of their children.
In these sacred responsibilities, fathers and mothers are obligated to help one another as equal partners.
Disability, death, or other circumstances may necessitate individual adaptation. Extended families should lend support when needed.
From The Family - a proclamation to the world:
I think Mormons are absolutely correct to emphasize complementarity of distinct domains within the 'standard' marriage rather than dominance-submission.
In any specific domain one or other sex has the responsibility; but neither has overall dominance; neither is overall required to submit.
(Complementarity of husband and wife is, of course, a fundamental part of Mormon theology; in that husband and wife both need each other for optimal theosis and progression to the highest Heaven or celestial kingdom. Also, note the important supplementary passage on the contingent need for individual adaptation.)
And this difference within marriage corresponds to my observation that Mormon women have a large, important and distinct role in the LDS church; while, by contrast, among traditional Mainstream Christians (such as conservative evangelicals) women typically have a very subordinate, less essential and indistinct role in the church - defined by exclusion and patronage - rather than an 'of right' complementarity.
Both the CJCLDS and traditional Mainstream Christians are patriarchal religions - but to formulate this in terms of 'submission' creates (I believe) a false, and sometimes hazardous, tendency for Christianity to collapse into the pattern of its most formidable rival - a patterns which is goes against the grain of Christianity's fundamental nature.
This tendency of traditional mainstream Christianity institutionally to marginalize women can be resisted, and often it has been and is resisted; but the tendency remains because it is theologically rooted.
NOTE: In the above passage from the Proclamation, I dislike the use of the word 'equal' because equal, in practice, gets to mean sameness; and the sexes are not the same - they just are complementary.
FURTHER NOTE: The mistake people make in this (and other) matters regarding complementarity is that they look for symmetry. In fact, complementarity is necessary precisely because of the lack of symmetry.
The primary thing about family (for Mormons) is motherhood, which can be defined quickly, simply, single word. Fatherhood is secondary and needs more words to describe. Women are (in essence) mothers, (worthy) men are priests - but motherhood and priesthood are not symmetrical. Very obviously not!
(For Mormons) Healthy women just are mothers, but men must be worthy to be priests. In the church the priesthood is primary, in the family motherhood is primary - but not in the same way. The priesthood and Relief society (the women's organization) are complementary in the church, but not symmetrical - and the priesthood is primary.
In Catholic Christianity celibacy is primary, men are primary - because men are priests. Motherhood comes below celibacy, and celibate female religious are not necessary. The church is necessary for salvation - but only men are necessary to the church: therefore women are not (religiously) necessary to Catholics.
In traditional Protestant denominations, the family comes above celibacy, but men dominate the family and the church alike, in a symmetrical fashion; because men are always the leaders and women must always submit (whatever the circumstances). In religious terms, men and women are individuals and equivalent in value. Women are not religiously necessary, but neither are men, except in the church - but (for Protestants) the church is not necessary.
And in Christianity's most formidable rival something similar prevails: all men submit to God, men have duties of worship, all women submit to all men, women are not religiously necessary.
Only in Mormonism are both men and women necessary and also the church necessary; but not to salvation, only to the higher levels of theosis.