I think even the second one is over-processed (of course this is somewhat subjective). Rainbows are exciting and make you want to take pictures, but are hard to get very vibrant in-camera. As suggested, a polarizer might help. I think the best thing to do with rainbows is get other interesting subjects in the frame with the rainbow so the rainbow is adding to other elements. Essentially, the Joe McNally rule of "standing in front of more interesting things" will make more interesting pictures. The sillhouetted trees are just not that interesting to me.

As a learning experience, maybe I would try a selectively increasing the saturation of the rainbow (can't remember if DPP does this).