It's all about the numbers
Once you get up above 1 TeV it doesn't matter so much whether or not you collide just matter or matter and anti-matter. The energy in a proton-antiproton collision is 4 GeV, about 1/500 of the kinetic energy of the accelerated particles. On the other hand, you can make millions of times more protons than anti-protons, so the "luminosity" of a proton-proton accelerator is much higher than that of a proton-antiproton collider. That's why the LHC doesn't use antiprotons.
They need the high luminosity to look for the "signal" of the Higgs.
There's a slight advantage in particle-antiparticle collisions in that the collision cancels all the quantum numbers of the particles and you get a cleaner result. If you want to make a particle like a Z boson from a proton-proton collision, you have to contend with all the quark debris, since the collision cannot turn quarks into something else. In an electron-positron collision, the result is pure energy, no residual particles. Proton-antiproton collisions are a bit messier, but still cleaner than proton-proton collisions.