The rim makes a significantly larger difference than spoke type. The rim is what connects the tire to the spokes, as well as creating a rigid point for the tire to be controlled with. Spoke type is less of an issue. Swaged (butted) spokes are stronger in terms of durability, but straight spokes are almost identical in terms of wheel strength. The proper wheel build and spoke tension is the important part. You can have the best rims/spokes/hubs around, but they aren't worth donkey unless they are built correctly.
So, to answer your question, the rim is a bigger factor that type of spokes in terms of wheel stiffness.
