The screwdriver in the "small size" Lumberjack (the silver-handled one) fits phillips heads quite well. It's a combination tool that opens tin cans too (though not as neatly as the dedicated type of opener). This screwdriver/combo tool is fairly slim, so it's best suited to "light duty" work.

As far as I can tell, the "full size" red-handled Woodsman (pictured above) doesn't have any tools besides the blade and saw.