Libertarianism is a social system, no need for it on a desert island. It gives man no guidance beyond how to deal with others.
Objectivism is an entire philosophic system covering metaphysics (recognises reality is real and cannot contradict its self), epistemology (recognised the use of reason as man’s only form of knowledge), ethics (personal morality of egoism, rational selfishness, i.e. pursuing your own values), politics (state protection of individual rights), economics (free market capitalism). All of which provides the framework for an individual to understand reality and make moral judgements in order to benefit his life, whether he is in a city of 30 million people or alone on a desert island.