We compare the average star formation (SF) activity in X-ray selected AGN hosts with a mass-matched control sample of inactive galaxies, including both star forming and quiescent sources, in the 0.5 < z < 2.5 redshift range. Recent observations carried out by PACS, the 60-210 μm photometric camera on board the Herschel Space Observatory, in GOODS-S, GOODS-N and COSMOS allow us to obtain an unbiased estimate of the far-IR luminosity, and hence of the SF properties, of the two samples. Accurate AGN host stellar mass estimates are obtained by decomposing their total emission into the stellar and the nuclear components. We report evidence of a higher average SF activity in AGN hosts with respect to the control sample of inactive galaxies. The level of SF enhancement is modest (~0.26 dex at ~3σ confidence level) at low X-ray luminosities (LX ≲ 1043.5 erg s-1) and more pronounced (0.56 dex at > 10σ confidence level) in the hosts of luminous AGNs. However, when comparing to star forming galaxies only, AGN hosts are found broadly consistent with the locus of their "main sequence". We investigate the relative far-IR luminosity distributions of active and inactive galaxies, and find a higher fraction of PACS detected, hence normal and highly star forming systems among AGN hosts. Although different interpretations are possible, we explain our findings as a consequence of a twofold AGN growth path: faint AGNs evolve through secular processes, with instantaneous AGNaccretion not tightly linked to the current total SF in the host galaxy, while the luminous AGNs co-evolve with their hosts through periods of enhanced AGN activity and star formation, possibly through major mergers. While an increased SF activity with respect to inactive galaxies of similar mass is expected in the latter, we interpret the modest SF offsets measured in low-LX AGN hosts as either a) generated by non-synchronous accretion and SF histories in a merger scenario or b) due to possible connections between instantaneous SF and accretion that can be induced by smaller scale (non-major merger) mechanisms. Far-IR luminosity distributions favour the latter scenario. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.Throughout the paper, the wording "inactive"/"active" refers to galaxies lacking/showing nuclear activity (non-AGNs/AGNs), regardless of their star formation rate.