I've never heard about a non deterministic theory in physics, classical physics is, quantum theory is (if I take the wave function of the universe its evolution is deterministic), general relativity is ...
And about the wave function collapse, it means that something not well understood happens when a system interact with another one which posses much more degree of freedom, it doesn't mean that something non deterministic happens.
Otherwise quantum mechanics would be self contradictory : if I take the wave function of the system {system I want to measure + rest of the universe} and use schrodinger the evolution will be deterministic, if I just take the subsystem {system I want to measure} and use the wave function collapse the evolution would seem undeterministic.
"Can you predict with certainty the result of, let's say, an energy measurement of a two-level system"
If I had the knowledge of the initial wave function of the universe and were able to calculate its evolution thanks to Schrodinger I would.
"Lastly, can you please elaborate the last part of your answer? I don't see how QM would be contradictory."
If I say "The collapse of the wave function means quantum theory is not deterministic" it would be contradictory with the fact that I can use Schrodinger on the whole system instead of using the collapse axiom and find a deterministic evolution.