Earlier quoted context omitted.
A simple example is (using the traditional understanding of these differences): Science-based: Cholesterol levels are associated with major adverse cardiovascular events (MACE), statins lower cholesterol levels and therefore statin therapy is recommended to reduce MACE. Evidence-based: A [specifically defined population] was given statin therapy or placebo. We observed lower MACE in the statin group, therefore statin…
> Cholesterol levels are associated with major adverse cardiovascular events > statins lower cholesterol levels and therefore You lost me here - because the science based one is just stating unproven statements to come to some conclusion. If you were to expand on why those two sentences are "proven" you'd likely come to evidence based reasons.
This is effectively the science based method, since it can be tracked to a, perhaps, 'plausible' mechanism (although often now lean towards more 'intriguing' than parsimonious, especially if published somewhere like Nature)
Evidence based medicine has other faults. One subfield is meta-analysis, which looks for very solid observations that are reproducible, but often lacks the complicated modeling that may be necessary to see any highly conditional effects. So the findings tend to be real, but boring and often "well-known". It is however, a good way to check if the "well-known" observations in the literature are reproducible.