I was co-supervised during my own Ph.D., and have since been a co-supervisor several times, and I find that if your circumstances are such that co-supervision makes sense, it can be an excellent thing.
Co-supervision makes most sense when either:
- You are doing cross-disciplinary work, and each supervisor provides expertise for their own discipline, or
- the two supervisors already work together so closely that working for one means you are de facto being supervised by the other already, and you might as well acknowledge it.
This can help in providing two perspectives (especially valuable for cross-disciplinary work) and in allowing you to get help from one when the other is busy or unavailable. The down side is that you may also find yourself being pulled in two different directions, and that it can be difficult to coordinate things that require approval from both two supervisors, especially if both are busy.
Most programs, however, will require precisely one person to be the primary supervisor, while the other is either listed as a co-supervisor or merely an unusually active member of your committee.