Before the post-conciliar renewal of the Lectionary, this passage from Ephesians was the first Scripture reading the people heard at the wedding liturgy. It’s still one of the options today. There is an option to just have the core of it, verses 25-32 proclaimed. But in either version, it’s not often chosen. The shorter version, while avoiding the female submission texts, focuses on the husband’s duties.
As I get older, I see less of what is objectionable in the entirety of this passage. In fact, this passage is likely the strongest Biblical expression of the sacramentality of marriage.
Let’s read it:
Brothers and sisters:
Live in love, as Christ loved us
and handed himself over for us.
Be subordinate to one another out of reverence for Christ.
Wives should be subordinate to their husbands as to the Lord.
For the husband is head of his wife
just as Christ is head of the Church,
he himself the savior of the body.
As the Church is subordinate to Christ,
so wives should be subordinate to their husbands in everything.
Husbands, love your wives,
even as Christ loved the Church
and handed himself over for her to sanctify her,
cleansing her by the bath of water with the word,
that he might present to himself the Church in splendor,
without spot or wrinkle or any such thing,
that she might be holy and without blemish.
So also husbands should love their wives as their own bodies.
He who loves his wife loves himself.
For no one hates his own flesh
but rather nourishes and cherishes it,
even as Christ does the Church,
because we are members of his Body.
For this reason a man shall leave his father and his mother
and be joined to his wife,
and the two shall become one flesh.
This is a great mystery,
but I speak in reference to Christ and the Church.
In any case, each one of you should love his wife as himself,
and the wife should respect her husband.
The late Father Joseph Champlin, in breaking open this reading, offers an insightful reflection:
Practical consequences flow from the sacramental nature of marriage. If the sign of the sacrament is this promise and the living out of the promise, then it follows that every time you are faithful, tender, considerate, every time you compromise or reconcile, every time you are thoughtful or unselfish, God’s grace enters your lives. Each time Christ becomes present in your midst, each time the Holy Spirit dwells in your hearts and in your home.
Lots of times couples choose a reading because they like how it sounds. You probably can’t go far wrong on that, I suppose. Some passages in the Bible are better written, more lyrical, and more appealing than others.
Another approach would be to choose readings with a theological side. The prime factor would not be how they sound, but what they say. This long-ish reading says a lot, implies a lot. Is a couple prepared to let Christ into their marriage to the point that the relationship reminds others of God? That is the high ideal of this passage from Ephesians.
So, if you can, get over the subordination. If you do, you have something lofty to which to aspire.
Catholic Sensibility 
In my meetings with couples, I usually include this reading in a talk I do about what it means to call marriage a sacrament. And I tackle the “subordination” issue directly by pointing out the line, up front, that usually gets missed: “be mutually subordinate to one another out of reverence for Christ” and also point out that when you understand the cross is the paradigm for this whole passage–when you realize it’s not about power, which is what is alienating, the idea that St. Paul is advocating male power over women, but about outdoing one another in surrender in imitation of Christ…then the whole passage takes on a different meaning.
I have had couples chose this reading for their wedding, so I guess I’ve had some influence.