I think that traditionally, it's the liberal/progressive main-line churches which emphasize the humanity of Christ to the detriment of his divinity. Jesus is a good teacher, a real person who fought for justice and cared for the marginalized. Even though sometimes this distinction is difficult to make because there is a simultaneous tendency to avoid gender-specific language or to see 'Christ' as an exclusive term, the distinction can still be made at some general level. They do a good job emulating Jesus in social and political realm--fighting for human rights, advocating environmental responsibility, pleading the case of the widow, etc.--but when it comes to actually talking about Jesus, missionally growing their churches, and developing spiritually formative practices such as prayer and devotional reading of scripture, they have trouble. They're good at emulating Jesus but they might have trouble surrendering to Jesus in a way which stands to reason.
On the other hand, conservative evangelicals tend to elevate the divinity of Christ until he becomes almost an ethereal concept rather than a flesh-and-blood man from Nazareth. This distinction is complicated as well because they don't see exclusive language as problematic. They have no trouble talking of Jesus and not just 'Christ.' The historicity (and thus, you'd think, the humanity) of the events surrounding Jesus' life are seen as utterly essential. But, nevertheless, it's common enough that conservative evangelicals hold to a more ethereal concept of the atonement. Jesus could have accomplished death and resurrection on some island in heaven because what really matters is not the political and social realities (i.e. oppression, poverty, racism, imperial conquest, etc.) surrounding Jesus but the substitutionary sacrifice, the resurrection, and the righteousness subsequently bestowed upon believers securing their post-mortem destination. They do a good job evangelizing (making sure others receive the same ethereal status) and boldly speaking about Jesus but they have a difficult time drawing real connections between the gospel of Jesus and the work of social justice. They're generally pretty good at developing spiritually formative practices such as prayer and devotional reading, or at least holding them in high value. They have a clear sense Jesus' divinity, so worshiping Jesus and surrendering to him are more naturally connected to their theology than actually emulating him and following his teachings. They understand surrendering to Jesus but they have a harder time emulating him in a way which takes this world's physical and immediate needs seriously. They can't help but be theologically drawn to the spiritual and 'eternal' rather than the actual faces of the people right in front of them.
If we can stand in the balance, if we can live in the tension, if we can value both the divinity and the humanity of Jesus, then perhaps we'd learn to surrender to Jesus while we emulate Jesus. Perhaps we would see Jesus as the good teacher who goes before us and as the God of the universe who saves us and invites worship from us. To affirm the humanity and the divinity of Jesus is to affirm the humanity of the people around us and to value them as those with whom the Lord of all creation shares identity... so that we can say, theologically, that social justice and environmentalism are important and that spiritual formation and surrendering worship are important.