Solasta does this on some level. You select a background for each character, and then you play through a short backstory for each different background (or class?) as a tutorial, and each different background also gives that party member a specific side quest in the main campaign later on. Plus, the backgrounds influence how the characters talk, what they say in conversations. It's still rather superficial on the whole though, not as involved as what you imagine.

Wildermyth also did a bit of that. Character traits influence what characters say and sometimes, I think, also trigger specific quests.

Are you sure? It's actually called Darkest Dungeon (there is no "The", my mistake). And it's a very well-known game.

In that game you hire party members between the raids into the dungeons. They don't have detailed backstory but they do have random qualities (quirks), some of which you can remove or add through special means, like visit to Sanitarium.

I think only people REALLY into character building would prefer the second option entirely. Ideally though a game has both, so you can fill a gap the provided companions don't or replace a companion you hate. For example in PoE I'm not a big fan of Durance, so I usually make a cleric to take along. I wish Dragon Age 2 had this option since they ridiculously provided only one healer and he's a very divisive character.

They can both be great. You can't really compare them when they're so different. Totally different type of storytelling.

I prefer #2. In Divinity: Original Sin (since it's been mentioned a few times above) I created my own two custom characters and did not take on any others in the course of the game.

That game should fall in between the two styles mentioned by the OP. But me personally, I think I would prefer for the game (Darkest Dungeon) to lean more to the second category, since a huge part of the characters can eventually be customized (for example, despite the fact that different characters of the same class would have different opening sets of skills, you can eventually unlock the other skills as you gain more gold), and for the characters' backgrounds, you can more or less use your imagination on how some of the characters got themselves there in the first place. Although there are comic strips explaining the backgrounds of the characters, it'd be kind of dull to think that all the characters of the same class come from the same origin. What I mean is, you can apply the official background to the first new character you get, and use your imagination for the next characters of the same class.

As for the OP's question, I'd say both. If anything, it'd be nice if you can customize your main character and have the other characters premade, since creating one character often already takes too much from me, and having to repeat the same process for the other characters would be too time-consuming.

Creating the entire party allows for optimal min-maxing, but I prefer just creating the main character and hiring/encountering the rest during the game. I like exploring stories, which is the main reason to play these kinds of games IMO. Just creating a stat sheet that corresponds to a Cleric and rolling with it is far less engaging than having to encounter a Cleric in the game first, having to do a quest for them before they join you, learning their backstory etc.


SPOILERS FOR DRAGON AGE ORIGINS BELOW!!!!


In Dragon Age: Origins for example, I ended up not accepting two companions into the party simply because of the stories/situations in the game. Sten, I didn't even realize was a possible companion and Zevran, because why the hell would I accept an assassin that tried to kill me into my party, IMMEDIATELY after failing to kill me :/
Would not have happened if I just created the entire party from scratch.