My supervisor wants to put someone else as first author on one of two papers when I have done most of the work on both. What should I do?
Generally speaking, it is infeasible for us to judge whether authorship or the order of authors on any given project is "fair", as all of those depend a great deal on discipline and the particularities of any given project.

That being said, from the little text you provide the 1/1 split does sound fair. There are two papers coming out of the work, one experimental and the other theoretical. The person who did the experiments first-authors the experimental one, the "theory guy" leads the theory paper. So far, so good, I would say.

You say that there was "nothing new" in the theoretical work. This seems highly unlikely to me, what would even go into the theory paper if that was indeed the case? In general, providing a solid theoretical basis to experimentally observed results is a very valuable contribution, that you maybe need to learn to value higher. Sometimes the theoretical methods to achieve this are straight-forward, but this does not diminish their value for your project.