It really shouldn't make a difference between those three passports - all will be $50 and the processing time the same. If you had a US passport in the mix, I would say do NOT use that - as it is much more expensive.

With only 12 hours in Nairobi why don't you just get an evisa in advance, rather than wasting extra time at the airport -http://evisa.go.ke/evisa.html - they do a transit one, and again, doesn't really matter which passport of the three you use.