How can two walk together except they be agreed. If you can't settle the matter, one of you do what is right by his conscience and the other does what is right by her conscience-- which would mean doing whatever the one who thought the break up was right though I suppose.
How experienced are both of you at hearing God? How do you know it's not your feelings or imagination? If you aren't confident in what you heard, then keep praying for clarity.
For my wife and I, getting direction from God to get married was very important to both of us. We had lots of clues. I was reading my diary, and I wrote down I believed the Lord had told me I'd meet my wife that month and that she'd be 23 years old. My wife was 23 when I met her that month. There were lots of little clues. I'd forgotten that my wife said that she felt like the Lord was speaking about the verse about cord the cord of three strands not being easily broken. Other people mentioned that verse to us during that time and I remembered that, but I forgot my wife saying the Lord had spoken to her through that verse. At our wedding party at my parent's house in the US, the pastor who prayed for us prayed a prayer that had a prophetic feel to it about a cord of three strands not being easily broken, where the third strand was Christ. So it's cool to look back at what happened and relearn all those details.
I actually had someone almost prophesying against me and my wife being together, not a prophecy, exactly, but her memory and interpretation of a vision. Because of that, I was in a bit of confusion over the whole thing, but it sure seemed like the Lord was telling me to marry my wife, and later, as I continued to pray and ask if it was His will, it sure seemed like He was saying, "Yes, why don't you believe Me?" which is a pretty serious rebuke, and thankfully He was merciful in helping me overcome my unbelief.
I would have loved to have gotten 'confirmation' of what I thought the Lord was telling me during the time I was making my decision. Eventually, I just decided based on all that it seemed like the Lord was doing and speaking to me, and I decided to get married, and then I was 100% sure and committed to it. My decision making process was over and I had plans to propose within less than a week. The next day after my decision, I went to a church meeting where the woman who had made the comment about our relationship was present, and someone prophesied over my wife and I about the Lord doing a work in us that would continue for many years, about going to many places and ministering to many people. It sure seemed like a confirmation of our marriage, and some of it has been fulfilled already.
If one of you is hearing marry and the other is hearing break up, fast and pray about it. Are the two messages necessarily contradictory? If one is 'marry' and the other is 'break up' both could logically be true, but it would require more time before getting married. If one thinks he hears "I want you to be married" and the other thinks she hears, "I don't want you two to be married" there is a problem.
I think fasting and praying is a good idea, as someone suggested, to get clarity. Has anyone else given you confirmation on it? What about less supernatural-sounding things like what each of your parents says of your potential choice for a partner?