Initially the slow reload rate put me off of the crossbow but when I decided to build a character around it, I fell in love with the power of it. then after the power shot and quick shot perks were added, it was just beautiful. I've been a stealth archer many times and now its hard for me to imagine using a bow again. never again will I have to worry about being ambushed while sneaking.
I've been using both while trying out No Snakes Alive's Demonhunter. I use the crossbow for long shots, dragons and strafing archers. The bows i use for rushing enemies such as wolves, spiders, and warrior types. With that strategy I'm nearly unstoppable (mages are still a pain)
I like being a BA with a crossbow. Them exploding bolts are just awesome. But I prefer the bow, with proper techniques it's possible to shoot 11 arrows into the air before the first one hits the ground, and this can be done with great precision while moving against moving targets. I realise this isn't the case in Skyrim, in which case I'll take my explosive bolts.
I find it to be situational, using bows in Skyrim allows for much quicker reloads so when facing a group of enemies I think the bow shines here, especially when perks are taken to increase the reload speed and you have Zephyr.
But when versing one or two opponent(s) the crossbow is just so brutal, especially up close just as much as at a distance. Using it from stealth just packs such a fierce multiplier of damage and having it ready-loaded lets you get that snap decision shot.
So you can move more freely in stealth, using silent rolls before you take a crossbow shot, where as a drawn bow doesn't let you silent roll.
i do have to point out one matter that hasnt been touched on i believe, load vs. reload, meaning to fire bow, u must draw bow, nock arrow, aim fire...with crossbow, draw, aim, fire... as far as first strike the crossbow has it and against surprise or fast moving enemies that can b the difference
Why choose a favorite weapon when you can have the best of two worlds?
I find it myself that even for roleplaying/realistic playing, it's possible to carry a bow and a crossbow.
Bow is best for spamming arrows, fast attacking, and to kill groups. Crossbow is best for armored enemies, barbarian-like enemies (You know, the ones with light armor and two-handed weapons who sprint towards you) and sneak shots.
I like using both. But honestly, I sort of hate crossbows. Do not get me wrong, they are nice and powerful, but I feel so awkward with them. One of the biggest things is the movement speed. When you have a crossbow in your hands, not even aiming or anything, you are very slow. With a bow you are completely mobile between shots. Another thing I dislike is their velocity. I find it hard to hit moving targets with crossbows even though the bolts go faster. Crossbows have their place, but I would always pick a bow over a crossbow.
I love the crossbow for a couple of minor reason, and one large one. I like how the bolts are less obtrusive and look attractive on a character's hip, I like how you can get exploding bolts, and how you don't have to be a smithing genius to be able to make the best kind of crossbow (unlike bows).
My favorite quality of the crossbow is that they are automatically loaded before firing. This makes them invaluable holdout weapons, useful to get a nice stagger hit against an enemy at mid-range, or to suddenly take down a fleeing enemy at long range. The bow takes longer to shoot since the arrow has to be drawn, and those valuable seconds can make the difference between fighting one enemy or fighting all of his friends in the rest of the dungeon that he just decided to wake up.