What would happen if we where able to split protons or neutrons?

Energy is same before & after splitting.

Together with the quarks there are gluons (jokingly named by physicists because of it's glue-like properties). They bind the quarks together and the more you try to pull the quarks apart the more force will bind them together. If you stretch enough it will become more energetically favorable to pull a quark-antiquark pair out of the vacuum rather than increase the distance.

Keep in mind that when I say 'pulling' I'm talking about smashing atoms together in facilities like CERN. The effects observed are therefore not some great energy release, but rather matter-antimatter particles in the detectors, and the energy bound in and released from these particles can never be higher than the energy used in the initial 'smashing'.

The great energy release you see from splitting atoms comes from early stars which have stored a part of their energy as large atoms. When we split these atoms we merely harvest the old stars' energy much like we harvest old sun-energy from oil.
There is no rule saying smaller splits give more energy. Unfortunatly.

I hope this was helpful. =)