What do I care?
This is actually the aspect of the debate that most interests me. What is at stake if we say evolution is God's method of developing us or if we say 6 days is pretty unambiguous? Neither of these options would ultimately affect our reading of scripture to any great extent. Whatever effects there would be, would come as we reinterpreted old scripture in light of new information. The church would continue to be true in either case.
So, what is at stake? Is it our unique place in the universe? Possibly. True application of Darwin's theories do not give humans much cause to point to themselves as the apex of evolution. Generally, the LDS who have partially accepted evolution as a means for God to create us seem to me to believe in a guided evolution. That God has tweaked the genes or the environment over time so that human body developed and could accept human souls. This is alien to Darwin's understanding and to modern applications of the evolutionary theory. The only guides for Darwin are death and reproduction, no supernatural invisible hands necessary.
Darwin wasn't hesitant to separate humans from animals though. One of the most important separators is the moral sense that humans possess that animals, apparently, do not. I talk about this with my students in terms of the shark (one of the more evolutionarily successful creatures ever). If we ignore human aesthetics, how do we distinguish between a good shark and a bad shark? Do sharks ever fail to live up to their moral potential? Is any shark (that reproduces) a failure? It is ridiculous to apply these categories to sharks (or other animals), but we readily do the same to humans. We are, in our minds if nowhere else, a different breed.
Some people have theorized that all of that moral handwringing and overanalyzation gives us an evolutionary advantage, which explains our place at the top of the food chain. Perhaps, but it hardly explains our sense of our own worth. We seem to feel ourselves apart from the rest of the natural world, but a greater likelihood to reproduce is hardly enough to give us this sense of superiority (or even the power to have this sense).
At the other end of the spectrum are the people who cling to a kind of Biblical inerrancy in describing metaphorical events and symbolic actions. This also leads us to a sure knowledge of our place in the universe. We are the chosen because God has chosen us and who are we to argue. We have a divine mandate to rule the earth, subdue it, and fulfill our destiny. We are the children of God and that conveys a status upon us that is unimpeachable.
The way we use both approaches leads us inexorably to the conclusion that we are special, which is not something that evolution proper actually does. Ultimately, I think this is why the Church has traditionally looked askance at the theological implications of evolution. I don't believe the prophets care at all if God took 6 days, 6,000 years, or 60,000,000 to develop us. They are understandably less willing to leave our development to the trial and error of natural selection. I don't think the Brethren it matters whether we came from hominids or other planets. But I do think that they believe that it matters whether God himself was involved in our development and in our lives today.
Ultimately, I have to reject evolution because it doesn't square with my understanding of a loving, involved God. Evolution is its own form of Deism. Darwin discovered the rules in charge, that God left the rest of the world to run by. But our success is not determined solely by whether or not we reproduce and God seems to be unwilling to let random chance and change be the sole determiner of how we become. So the standard evolutionary theory doesn't accurately explain my spiritual experiences and, ultimately, that is the only evidence that is convincing to me.