From the perspective of a wildfire exposure (ember or flame), a narrow overhang is arguably better. Your home will experience other exposures during its life, however, which you should consider. As shown in this photograph, a wide overhang is a much better option for protecting exterior walls from rain - the wider the better.

In this photograph the wider overhang on this home provided complete protection to the wall during the rain shower.

This figure shows the results of a survey of homes that was funded by the Canada Mortgage and Housing Corporation (CMHC) and published in 1996. The y-axis shows the percent of homes surveyed that had water related problems. The x-axis is the width of the overhang above the exterior wall. This graph shows that more water-related problems were associated with walls having narrow overhangs.

This is another example of the protection from rain provided by a wide overhang, in this case the head the window. The darker (lower) portion of the wall has been wetted by rain.

A wider eave can be protected from wild fire exposures by using ignition resistant or noncombustible materials. In this case the overhang (on the rake end of the building) is protected by stucco that was wrapped around and under the eave.