The growth parameter dependence of the transition from 2D to 3D growth of GaInAsP multiple quantum well (MQW) structures up to epsilon(B) = 0.5% tensile-strained barriers was examined. Identical MQW structures with epsilon(W) = 1% compressively strained wells were grown by metal organic vapor-phase epitaxy (MOVPE) and metal organic molecular beam epitaxy (MOMBE) and characterized by photoluminescence (PL), X-ray diffraction and transmission electron microscopy. Increasing the tensile barrier strain resulted in deteriorated optical and crystalline properties beyond a critical strain limit, which depends on growth temperature. The deterioration originates from lateral layer thickness and strain modulations. Their density, amplitude and thus their effect on the optical MQW properties are different for both growth methods. High-quality MOMBE-grown MQW structures up to epsilon(W) = 2% compressive well strain and epsilon(B) = 0.5-1% tensile barrier strain could be achieved by inserting thin intermediate layers at each internal interface. The composition of these intermediate layers has a significant effect on MQW material properties.