I have seen the following information a few different places, and it raises the question for me:
If the hand crossbow requires two hands to use–one for shooting, one for loading–then is there any benefit to using it over a two-handed crossbow?
You still need a free hand, so you can't use a shield or a second weapon, and you can always hold a two-handed crossbow in one hand while you grab something else or cast a spell.
Ammunition and Two-Handed errata
A couple of things that have basically been how I’ve been playing things, but good to see them officially in the rules. You need a hand free to reload a one-handed weapon with the Ammunition property. (It needs two hands). Also, although the maul and other two-handed weapons might require two hands to attack with, you can hold those weapons in a single hand.
This second clarification makes a spell-caster casting Somatic spells have an easier time with it when also wielding a two-handed weapon.
Best Answer
There are a variety of reasons to use hand crossbows!
Combat practicality. The Crossbow Expert feat grants that sweet Bonus Action shot with an already-loaded hand crossbow. Even without that, holding one in each hand means you aren't held down to the one-attack-per-round drawback the Heavy and Light crossbows suffer due to the Loading property.
Inconspicuousness. Maybe you need assassinate the Evil Count at the Grand Ball? That big, Heavy Crossbow's not gonna pass the guards' ocular pat-down, but the Hand Crossbow in your big, fancy coat might get by easily. Maybe you want to back up your buddy in the standoff in the bar? Lugging out your big 'bow is slow and gives everyone time to react, but you can relatively realistically quick-draw with your hand crossbow (assuming you thought to have it strung and a bolt ready, for whatever reason).
One hitter... ness. If you're looking to set up an ambush, having that single shot ready to go can be very worthwhile. Drow, for instance, are notorious in game for shooting from a hiding place with a poisoned hand crossbow bolt before closing to melee, a fighting style that works very well with the HCB/Shield combo. The light crossbow might do slightly more damage, but it'll take another action to strap on that shield while the bugbear you just cheesed off is charging down on you.
But ultimately, it's a cool character concept. If you want to play a gunslinger, or a pirate, or fantasy Trinity from the Matrix, having a long crossbow sorely clashes with the core of a character who would rather carry a revolver or a flintlock, or just a bunch of throw-away guns, one handed.