Personally, I think this is a very good question (I ask this to myself all the time).
I have a higher degree but I don't necessarily want to meet someone with the same kind of degree (not that I am not open to it) since I have other interests and needs. A friend of mine told me once:
- There is not a single Lady on this planet that will marry you neither because you know how to solve differential equations nor because you pray the rosary in Latin. She will marry you because she will be attracted to your cheerfulness, your personality, because she feels you know how to love and care, but most importantly because you prayed for it!
The same thing applies for me: I won't marry someone because of her degree, but because I will know that she is able to love me and understand me. Because we share similar interests (not academic) but related to family issues, e.g., building a future for our kids. I would marry her because we enjoy spending time talking together (on diverse topics, including topics that needs some thought and analysis) and we can solve our differences. I will choose to marry her because we will be able to live a good Christian life (and why not? because we will be able to become saints despite our many faults). The main problem is that we "men" tend to look first at other things that are important but not the most important things (such as physical attraction).
Now returning to the topic of the degree difference:
I think that a degree matters, and not for the reasons you think. It matters because it becomes an obstacle to develop a good healthy relationship. People with higher degrees, in particular, some of us dedicated to research, tend to spend time alone (we need space to think about problems), and we have been trained to be analytical in our thinking. The problem is that this becomes part of our personality.
For instance, sometimes we seem to be arrogant when we discuss topics (and in any relationship you will have to discuss personal issues, or even argue over disagreements), we sometimes don't intend to be arrogant but we feel that we are not being fully understood. This doesn't imply we want a PhD person to be able to discuss things at the same level; rather we look forward to meeting someone who is patient enough to listen and who can clearly explain us when we are wrong!, this requires a person with character, who is self-confident and charitable (BTW. PhD's are so specialized to a particular topic that they know nothing about what is going on in the world outside the specific research topics). This is a big issue for me!
Also, because we tend to be too focused on our research, we tend to be less social (which is not the same not being sociable, I love talking to people and getting to know them at the personal level). The problem is that we don't have much time to socialize (or at least we tend to think we don't have much time for that)! Hence, we end up missing some gatherings, or simply cannot afford going out every single weekend! (BTW. I feel attracted to sociable women, which is kind of a big problem, I don't have much time to keep up!)
On the other hand, I can say that many of my PhD friends who got married before getting a degree and who are very happy even though their spouses may have only a bachelor degree. The reason is because they love each other, and not the degree! And I also see many of my PhD friends who got the degree first and are having such a hard time getting married.
I hope this is useful,