As far as empirical truth goes, I agree. However, what if there is no objective reality? What if the core tenets of empiricism demonstrate themselves to be false?
Moreover, how is it that we arrive at empiricism to begin with? We arrive at it through the logical analysis of our experiences. We come to inductively conclude that there is a coherent, external reality independent from our own existence. That is a perfectly logical conclusion, but it is a conclusion of logic, not empiricism. It is the start for empiricism.
And what about when empiricism conflicts with opposite models, such as solipsism, idealism, or dualism? How can one compare them? It's logic that tells us to favor the empirical approach.
What about when certain empirical findings are illusions, confabulations, or hallucinations? What corrects for these errors? Not empiricism itself, but the logical analysis of empirical evidence.
This is why I think logic is the superior method. It could one day be essential in improving upon empiricism to turn it into something more accurate. Plus, as mentioned before, it doesn't dismiss other fields that science relies on, such as mathematics.
Empiricism carries with it implicit assumptions, whereas logic is a pure methodology.