Hi Fenriz - I'm sorry, you were correct! It was I who got confused between ALICE (a LHC experiment) and ALEPH (a LEP experiment)! The names are too similar. However, as you rightly state, ALICE (and LHCb for that matter) is a relatively small experiment. The main two general purpose experiments are ATLAS and CMS. You can call them competitors really - they've been trying to outdo each other for years, even before the beams started. Each of these big experiments has around 2000-2500 particle physicists. When they will publish anything, the author list will be about as long as most papers!
I will try to explain the difference between electron-positron and proton-proton colliders. Please ask me if anything doesn't make sense. Firstly the principles behind colliders. When we fire one particle into another, they collide at a certain energy, annihilating one another. This energy must go somewhere, and can result in other particles being produced. As energy must be conserved (you cannot take out more than you put in), the maximum energies of the produced particles cannot exceed the energy of the collision. How can mass and energy be compared in this way. Well, in particle physics we use natural units (electronvolts - our energy scales are gigaelectronvolts, or GeV for short), hence we are able to compare mass and energy. This is a very simple explanation, and there are many things I have left out. I'm just not sure how to explain it before I start to confuse everybody... and myself... just assume mass = energy, which isn't true, but for all intents and purposes it is - otherwise I will have to talk about momentum, and I might as well send a copy of my PhD thesis to all of you...
As the electron and positron are fundamental particles (ie. they cannot be broken down into smaller pieces), the products of their collisions are very easy to deal with. This is because if you fire an electron beam of energy 50 GeV against a positron beam of energy 50 GeV, the centre-of-mass energy (energy at collision) is 50 + 50 = 100 GeV. Every collision will be of this energy. Therefore, the particles produced in this collision cannot exceed a total mass of 100 GeV.
However, electrons and positrons (positrons are the antimatter particles of electrons) lose energy through bremsstrahlung radiation losses when they follow a curved path. The 27 km circumference accelerator ring, like the one at CERN, is such a circular path. As you put more energy in, the radiation losses get worse, until you reach the point of diminishing returns. The LEP collider was run at the maximum energies possible for a ring of its size - I think 200 GeV centre-of-mass energy - for the last period of its life.
Enter protons! Protons don't suffer such losses as they are more massive. Therefore, the highest energy possible at collision is 14 TeV at the LHC (14 TeV = 14000 GeV). However, they are not fundamental particles - they are made up of quarks. It is the quarks that collide, and as the total proton energy is shared among the quarks, the actual collision energy could be anything below 14 TeV - there is a wide range of possible energies. This makes the analysis more complicated.
Another problem is the fact that quarks, outside the bound state of proton, are unstable. Hence, if two quarks collide, the protons are destroyed, and the other quarks that were not involved in the collision "decay", creating more particles. These particles are not part of the collision, and must be removed, adding another complication to the analysis.
Therefore, higher energies are possible with proton-proton collisions, so we can detect particles of greater mass. However, electron-positron collisions are easier to analyse, allowing for more accurate estimations of particle properties, such as mass. They compliment each other - proton-proton colliders give you an idea of where to look for a new particle, and electron-positron colliders allow you to study that particle in more depth.
Was that really complicated? I tried really hard to explain that in an easy way, but I don't think I've done a very good job. Please tell me if there is anything that you don't understand.