Undercoat or Paint underside of body

[fakesnake.com]

I am getting ready to pull the frame on one of my projects to do some welding work on the frame. I figured I would paint the underside of the body while I had it off the frame. I took it to the local shop and they recommended undercoating. Their opinion was paint will chip easily being suceptible to rocks. I have some of my friends saying to paint it as undercoating may not look that great over time.

Any opinions? It won't be a trailer queen or riddler mobile. I plan on driving it but it will be a nice custom ride when I'm done with it.