The worst possible physical pain is far, far, far more intense than the worst emotional pain, but I think that in general emotional pain is more likely to last longer. I voted physical, because at any one point in time it would be worse to be in the worst physical than the worst emotional pain.
But I'm not sure if that's the best criterion. You could say that the worst kind is the kind that has bothered you the most during your life, and I think that for most people it will be emotional pain. A lot of people will lose a loved one, have their heart broken or feel depressed, but most will not likely be tortured or severely burnt, and even if they were (and lived to tell the tale), it seems likely that they would have suffered some emotional pain in addition to the (at the time much worse) physical pain. And even in less extreme situations emotional pain can easily accompany physical pain: If you break a leg before an important tournament you may feel very disappointed, or if you are beaten up you may end up being too afraid to go outside after.
tl;dr: The worst physical pain is worse than the worst emotional pain, but I think most people are more likely to experience (and dwell on) emotional pain that is more towards the really bad end of the spectrum.