One calculates the differential cross section for a particular scattering process using the standard model. This essentially gives the probability distribution for that process.
If the process is mostly QED - e+e- -> e+e-, mu+mu-, etc, then the cross section is well known. (In fact it's one of the first calculations one does in a particle physics class). If QCD is involved, it can get ugly.
Your question about proton / antiproton collisions mostly making pions, while electron / positron collisions mostly making photons deals with the fascinating subject of the difference betweeen "electromagnetic" showers and "hadronic" showers. The differences in rest mass is not the answer. You can accelerate electrons and positrons up to energies far in excess of the rest mass of the proton, and still the results of the collision will give fewer hadrons than a proton / antiproton collision at the same energy.
This is a fact that is well known to people who read papers on cosmic rays because one can distinguish the primary particles in cosmic rays by looking at the ratio of hadronic (i.e. pions) to electromagnetic (i.e. photons, electrons and positrons) in their showers. I just finished an outlandish paper that touches on this subject: http://www.brannenworks.com/PHENO2005.pdf
An intuitive explanation (that is wrong in that it ignores gluons and stuff) I've seen for the extra pions produced in hadronic interactions, is to say that at short distances, the quarks act like free particles. So when you have a collision between protons, the 6 quarks involved are very likely to end up split in ways that are not color neutral. For example, three quarks might go one way, one another way, and the other two in a third direction.
There is no problem with such a collision at first, but if the debris is not color neutral, and since the color force increases with distance, the separating quarks cause the vacuum to make more quark antiquark pairs. So all those extra pions get extracted from the vacuum by the color force.
Since leptons don't have color charge, their collisions don't make nearly as many pions.
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