For the sake of argument, assume the LHC was able to accelerate / focus / collide neutron beams, with the same energy levels it runs at for p-p collision.
Would the collisions produce any major differences vs the p-p collisions?
Is there a major difference between neutron-neutron collisions compared to proton-proton collisions?
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Major differences no, because what really collides are constituents of the protons (called partons): the valence quarks, the quarks and anti-quark due to quantum fluctuation and the gluons. The same thing happen with neutron.
However, since in proton $u$ quarks carry more momentum than $d$ quarks (because proton contains 2 $u$ valence-quarks and 1 $d$ valence-squark), processes involving u quark happen more likely. For example $u \bar{d} \to W^+$ happens more often than $d \bar{u} \to W^-$. If neutrons collide instead of protons, the situation will be the opposite. It would be easier to get $d$ quark with large momentum, the neutron containing $ddu$ as valence quarks. Hence, more $W^-$ would be produced.
So in conclusion, no major differences, but generally speaking, all charge asymmetries would be opposite.
