Why is beta negative decay more common than beta positive? In simple terms, why is beta negative decay more common than beta positive? 
I know it's something to do with occuring inside/outside the nucleus - but I can't find a simple, easy to understand explanation!
 A: The beta-decay may be "locally" reduced to a decay of a proton or a neutron inside a nucleus. The beta-minus decay contains the microscopic process
$$ n\to p + e^- + \bar \nu_e  + O(1{\rm \,MeV})$$
where the last term indicates the rough increase of the kinetic energy of the decay products. On the other hand, the beta-plus decay contains the process
$$ p  + O(1{\rm \,MeV})\to n + e^+ + \nu_e  $$
which means that the proton has to acquire some extra energy if it wants to decay to a neutron and a positron. In realistic beta-plus decays, it takes it from the surrounding nucleons in the nucleus.
Obviously, decays to lighter products where the energy conservation allows to give the final products some extra kinetic energy are more frequent than decays which only occur if an extra energy is found at the beginning. For example, among the bare processes above (for free nucleons), only the decay of the neutron may occur. The proton is stable (ignoring very infrequent processes linked to grand unification).
At the end, the inequality between the two types of the decay boils down primarily to the fact that the neutron is heavier than the proton which subsequently boils down to the fact that the down-quark is heavier than the up-quark (the rest masses).
A: Beta-minus decay occurs in nuclei with an excess of neutrons, while beta-plus decay takes place in  neutron-deficit  nuclei. A lot of natural background radiation on Earth is due to fission or alpha-decay of  heavy radioactive elements. The remains of  fission or alpha-decay are neutron-rich nuclei, so beta-minus decay is more common on Earth. 
Whereas on stars beta-plus decay is typical, because  neutron-deficit nuclei are produced in nuclear fusion.
A: (The following extends Georg's remarks earlier, where K-capture refers to K-electron capture.)
Beta-plus decay competes with electron capture, but there are few positrons around for beta-minus decay to compete with, so even when beta-plus decay is possible, its branching ratio may be small or overwhelmed by EC.
Moreover, in EC (versus beta-plus decay) the energy difference between initial state and final benefits from the addition of an electron to the reactant side and loss of a positron on the product side (so about 1MeV total).  So some nuclei decay by EC that can't decay by positron emission. 
