  Two-pion exchange parity-violating nucleon-nucleon interactions from recent
effective field theories and earlier fully covariant approaches are
investigated. The potentials are compared with the idea to obtain better
insight on the role of low-energy constants appearing in the effective field
theory approach and the convergence of this one in terms of a perturbative
series. The results are illustrated by considering the longitudinal asymmetry
of polarized protons scattering off protons, $\vec{p}+p -> p+p$, and the
asymmetry of the photon emission in radiative capture of polarized neutrons by
protons, $\vec{n}+p -> d+\gamma$.
