Papers from different authors with similar results submitted to the same conference
This sounds like a straight-forward case of multiple discovery.  

In the case that both papers are well-written and have correct proofs, the typical and appropriate thing would be for both of them to be accepted.  If one or both are not sufficient for the standards of the conference in their presentation or technical approach, however, then it would be reasonable for one or both to be rejected, however, even if they have identical results.

Given that there is often a great degree of variability in reviewing, however, it would likely be a good thing to get in contact with the conference organizers and let them know about the situation, so that they can ensure fair treatment of the two papers (e.g., via meta-review or by assigning the same reviewers to both).