I can not speak to the effects of wood on a firebox. As regards coal versus oil a firebox is subject to wear on the fire side due to expansion and contraction and abrasion. An oil fire can change volume and intensity in a fraction of a second. If the fireman shuts the firing valve while the engine is working "cold" air will be drawn through the firebox and the tubes causing thermal shock. On a coal burner these changes occur much more slowly. Remember boilers and their fireboxes are essentially balloons. repeated expansion and contraction wears them out.
In my experience oil burners show more firebox cracking and stay bolt failure than coal burners.
As regards abrasion the oil fire does not cause abrasion although "sanding" the flues abrades the soot off the sheets. The cinders from a coal burner keep the soot largely removed from the sheets. The primary areas in which I have observed abrasion is on stay bolt heads. In my experience I have not witnessed significant head erosion with properly applied stay bolts.
Generally speaking my experience is that proper firing of oil burners is less physical but more demanding than coal burners.
Due to human factors (less than perfect firing technique) oil burners have shorter firebox life than coal burners. This of course assumes that water and demand factors are equal between the locomotives being compared.
I guess we need to compare both fuel types on similar locomotives operating over the same territory to draw stronger conclusions.
John Bush