We present a comparison of epitaxial designs for non-resonantly pumped vertical external cavity surface-emitting lasers for emission in the red spectral range around 665 nm. Here, the VECSEL chip is based on a metal-organic vapor-phase epitaxy grown (GaxIn1-x)(0.5)P-0.5/[(AlxGa1-x)(y)In1-y](0.5)P-0.5 multi-quantum-well structure with 20 compressively-strained quantum wells. The wells are placed in packages in a separate confinement heterostructure with quaternary AlGaInP barriers and cladding layers, respectively. The active region is fabricated on a 55 lambda/4 pairs Al0.50Ga0.50As/AlAs distributed Bragg reflector. We compare two designs with different quantum well distributions in the chip: one design which includes 4 quantum wells in 5 packages whereas the other contains 10 quantum well pairs to have a larger absorption length. Laser parameters like output power, differential efficiency and threshold pump power of the different chip designs measured in a v-shaped cavity configuration are examined. By using the 10 x 2 quantum well distribution in the chip, we could improve the absorption efficiency by nearly 40% and output power by 25% compared to the 5 x 4 design. Additionally, by introducing tensile strained quaternary barriers and cladding layers in the 5 x 4 QW design, we could compensate for the compressive strain introduced by the quantum wells. Photoluminenscence measurements of structures with different numbers of quantum well packages reveal a more homogenous quantum well growth due to the strain-compensation technique. Furthermore, with the strain compensation technique, the output power could be increased over 30% compared to our conventional structures.