At present, diblock copolymer phase behavior in the long-chain limit is considered to be governed by three factors: the volume fraction of one block, phi; the segregation strength of the diblock, chi N; and the conformational asymmetry parameter, epsilon. This implies that the phase diagrams for polymers of different chemistry but similar molecular weight should evolve simply and smoothly as epsilon is varied. We present here partial phase diagrams (covering the cylinder-gyroid-lamella region) for two derivatives of the well-known styrene-isoprene diblocks: styrene-(ethylene-alt-propylene) and vinylcyclohexane-(ethylene-alt-propylene), all of similar molecular weights. Comparison of the S/I, VCH/EP, and S/EP phase diagrams reveals that the phase behavior does not vary simply with epsilon. In particular, the shape and extent of the gyroid region differ greatly between the three chemistries; in the S/EP system, this region disappears into a cusp at moderate segregation strengths (chi N approximate to 24). Our findings indicate that factors other than phi, chi N, and epsilon do influence the free energy of diblock copolymer mesophases and their regions of stability.