Brick and earth ovens

Perhaps a silly question, but is there an advantage to using wood to fuel a brick oven over gas. I get that there can be a subtle smoke flavour imparted possibly, but with natural gas running so cheap, why would one not use this as the heat source? Does wood burn more intensly, thus more efficiently in getting to temp?

It seems that if gas was used as a source, a more steady temperature could be achieved, less particulate emitted, and once oven up to temp, would use little gas if any?