without looking at your HMS setup, it would seem you have not properly considered the stream flow in HMS that is likely causing the faster response time and higher peak in RAS. Also you need to make sure that the mannings roughness used in RAS is a reflection of your HMS catchment setup. I have done many rain-on grid RAS runs and found very close matches to hydrologic packages such as DRAINS that we use here in OZ.
The other thing to check is the volumetric runoff, this will tell you if you have setup HMS properly to match RAS.