PAN;
This is a difficult question to answer because of the number of variables involved in selection of material for service – design temperature, pressure, environment, and cost of material and ease of fabrication, etc. Typically, on a first cut basis, the choice of using either 1.25% Cr-0.5% Mo or 5%Cr-0.5%Mo is driven by service temperature and/or corrosion environment in boiler and pressure vessel service. The higher chrome alloy will offer increased resistance to oxidation and sulfidation, and but may have slightly lower allowable stresses in comparison to the 1.25% Cr-0.5% Mo steel at elevated temperature.
My first suggestion is to obtain or get access to an ASME Boiler and Pressure Vessel Code, Section II, Part D Allowable Stress Table as a guide for comparison of material allowable stress values at the desired service temperature. A proper comparison can be made between the two alloys, which does not take into account corrosion.
As far as suitability for corrosion service, the driver here is environment. The petrochemical folks should be able to provide some direction for source of information. I do remember that higher chromium is beneficial to reduce exposure to attack from sulfidation, but the main benefit I have seen from my experience is that chromium enhances oxidation resistance in these alloys for use in power boilers.