It's clear that some sort of theological agreement is important in these sorts of relationships--though just what level of agreement is needed isn't quite so clear. Theologically, as Lutherans we don't believe that we all have to agree on every jot and tittle in order to have unity in the Church. Article VII of the Augsburg Confession states that “the true unity of the church” is present where the Gospel is rightly preached and Sacraments rightly administered. And I for one think that is right on. So its not surprising that we should be seeking these sorts of relationships even where there are theological disagreements. But as a student of Lutheran theology and the Lutheran Confessions it seems to me we haven't spent a huge amount of time on what "rightly" means exactly these days on either the Gospel or the Sacraments, or how that impacts these agreements. I think the hope is that we'll figure it out as we go along, but it does seem that some of the theological debates about the Lord's Supper that raged in the 16th century actually had some valid differences that shouldn't be so quickly overlooked (though we can play nice and probably not need to kill one another over them anymore.)
The biggest difference from where I stand comes from some of the secondary conclusions that come from a the different views of how Christ is present in the bread and wine of communion. In a more symbolic understanding (ala Reformed, especially following Zwingli) where the act and elements of communion are understood merely to "remind" one of the Last Supper, or of Christ, or are some other sort of symbolic reenacting for our remembering sake, we loose something of the power and mystery of communion. The underlying assumption is that God (who is essentially holy and in charge) doesn't fool around with ordinary stuff like bread and wine, or if God does, its only to bring to mind more lofty things. The Reformation era version of this view was something along the lines of "How can Christ be present in two places at once? He can't be at the right hand of God and in the bread and wine of this table. This "stuff" just reminds us of Christ who is enthroned on high." But as Jane Strohl, my professor at PLTS, once remarked "Its not as if the right hand of God is a folding chair!" Lutherans tend not to get bogged down in the spacial nature of this whole deal, and are willing to embrace a bit of mystery (i.e. if God really is God, then don't you think God could figure out how to many places at once?). But there is more to it than that.
One of the most important things (I think) about the Lutheran understanding of how Christ is present in communion is precisely that God does mess about in ordinary things like bread and wine, and would step down from on high to become present to us and for us, even though we are jerks. In fact while we assume that "on high" is where we ought to look for God, in fact God is really found in low places where God is most needed--among the poor, the suffering, the outcast, and when we are at our worst. This concept is referred to by theology nerds as the "Theology of the Cross" (or for the uber-geeks Theologia Crucis) and is one of the main reasons I love being Lutheran. And, in one of my favorite Luther "quotes" that nobody can ever seem to find in print, Luther contends that because he has been able to experience Christ present in the bread and wine of communion, he is able to experience Christ in his pea soup--meaning in the everyday stuff of human existence. Luther (and Lutherans) insist that God is essentially "incarnational"--meaning "enfleshed" or "embodied" or otherwise deeply connected to the ordinary stuff of human experience--and that's how we experience God: in, with, and under ordinary stuff. We've tended to call this "real presence" meaning Christ is really, truly, actually present in the elements of communion, even if we have no freaking clue how this actually might work on a technical level.
So its hard for me to see how we can be in "full communion" with denominations who don't share this fundamental understanding of how God works in relationship to creation, to humans, and to the bread and wine of communion. I haven't read too deeply about the agreements of 1997 (UCC, Presbyterian, and Reformed) or how these things have been talked through, but my guess is that they really haven't. The Episcopal church, following more closely the Roman Catholic tradition from which they came, seems closer to this Lutheran understanding. And, to be honest, I know pretty much zilch about the Moravians (do you?). And then we come to the Methodists.
Now I don't know all that many Methodists, nor have I experienced a wide variety of Methodist worship, but from the folks I know and the services I have attended, it doesn't seem like communion gets a lot of air time. And my impression of their theological understanding of communion are pretty much in line with those of your general American protestants (aka Reformed) and more along the lines of "symbol" than any sort of "real presence" or "incarnational" understanding. So knowing that we've been able to work these things out (or maybe just get by without talking too deeply about them) with our Christian brothers and sisters from the Reformed tradition (I'm including the PCUSA and UCC here too) it didn't come as too much of a surprise to me that we had reached the point of voting on an official Full Communion relationship with the United Methodist Church.
I know full well that this agreement is very likely to pass without much issue at the Churchwide Assembly (I imagine we'll be so relieved to not talk about sex for 20 minutes that we'll gladly pass anything) but I did think it was my duty to look fully into this whole thing and figure out if I actually thought it was a good idea and whether I could, in good conscience, vote for the thing. Now, my inclination is towards closer relationships with Christians of any and all theological viewpoints (didn't Jesus pray that we all would be one?) but when we are talking "Full Communion" I want to be sure that I'm being faithful to the Lutheran Confessions and their understanding of "right celebration" as important for unity in the church so that our "communion" might actually be as "full" as could be.
So I must say I was pleasantly surprised to read the statement on communion that the UMC put out a number of years ago. It is really quite compatible with the Lutheran understanding though we each emphasize our own favorite things: holiness for the Methodists, human depravity (and Grace, don't forget Grace) for the Lutherans. I'd suggest you check it out yourself (you can find it here). The Lutheran version of the same sort of thing can be found here.
It was also kind of fun to realize that the same sort of practical issues that affected the weekly practice of communion for my Lutheran pietist ancestors are shared with our Methodist brothers and sisters. The lack of clergy led to less than weekly communion in most congregations (they only got a pastor in town once a quarter out in the heartland when he rode in for the weekend). This led to a change in how it was understood, how it was practiced, and the overall point that was communicated. Both groups are rediscovering weekly communion, putting it back in the center of the worshiping life of our Christian communities, and a reclaiming some of the theological implications that have slipped away. I think we have more in common that either group probably realizes. That, it seems to me, is what ecumenical relationships are meant to be all about.