This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants of the local constancy and descent axioms. The main result is an equivalence theorem between (Cauchy constant and additive) algebraic quantum field theories and (Cauchy constant, additive and time-orderable) prefactorization algebras. A concept of ∗ -involution for the latter class of prefactorization algebras is introduced via transfer. This involves Cauchy constancy explicitly and does not extend to generic (time-orderable) prefactorization algebras.