So, longbows have a bonus against flyers (especially the ranged slaying demons) and crossbows have a bonus against people in melee range. I don't want my ranged units in melee range, so I am starting to think it is better to just always use longbows (except possibly with Tetike - they are inherently short ranged and may be in melee range more often). What do other folks think?

I prefer longbows overall. Flying slayer is actually useful in my games where the AI tends to assimilate Kazanji and Nidya when they can. In terms of raw stats, longbows have higher damage overall and sometimes have higher initiative, if you're using something like a glassteel longbow. I prefer the higher damage over the defense you get with a crossbow and shield since I mainly use archers for kiting or use them behind a wall of melee troops.