Two PhD students named 'Theory' and 'Experiment' are working on a project. Both are experimentalists by training but, from experiences working on a separate project, Theory comes up with an idea for a new experiment. Positive results from this experiment would have a small but significant impact on their field. However, Theory does not have expertise on the particular instrument required to conduct the experiment so, with the blessing of their adviser, Theory enlists Experiment who is an expert at using the instrument. Theory guides the experiment but the execution is all done by Experiment.
Happily, the results are positive!
The question is, given that Theory and Experiment agree to share first authorship, who should be listed first?
Edit: after writing this I found this thread Had the idea vs. did the work: Who should be the lead author? which is very similar to this question.
There's also an interesting discussion of the issue in this blog: https://funkdoctorx.wordpress.com/2012/02/27/co-first-author-and-cvs/