1. The game provides you with pre-made party members, each with their own backstory, dialog, and perhaps side quests.
2. The game lets you create every party member, leaving their personalities up to the player's imagination.

So, between these styles, which do you prefer? (Examples of 1 are Final Fantasy 4 and Baldur's Gate 1 & 2; examples of 2 are Dragon Quest 3 and Icewind Dale 1 & 2.)

It probably won't surprise you that I'm opting for the middle ground again, or the classic "it depends on the game", instead of your "either or". I'd say, ideally a bit of both, e.g. create 3-4 characters yourself, allow 2-3 pre-made companions to join on top of that. Generally, creating my own characters is more fun to me in terms of combat and progression. If given the choice, I'd always rather pick classes and attributes and all that myself instead of leveling up characters I did not create (and most likely would not have created the way the developers did). So gameplay-wise I feel closer to party members of my own creation. But I like games with good storytelling, too, so if the companions are well written, letting fully developed personalities into the party can be fun as well.

The challenge with a type 2 game is encouraging the player to view the party as actually having personalities, rather than simply a collection of stats. Blobber-style games tend to fall into this extreme.

Or perhaps I simply lack imagination...

Divinity Original Sin did this well. You didn't create the characters, but you did customize their abilities and stats.

First time playing through -> pre-made party members with zounds of background story and dialogue and party interaction.

Subsequent playthroughs -> Custom party members for optimised efficiency and powering through extra challenges.

For example in the Pillars of Eternity games. There's a book's worth of storytelling there amongst the pre-made party members, but you'll have an easier time in combat with optimised custom party members.

I have no preferences in that regard.
It all depends on the game and what kind of story it tries to sell to me as the player.

If the group "has to consist" of certain characters to make the story work (think: The Witcher, etc) - pre-made chars are totally fine.
If the story isn't bound to a certain set of characters (think: Pool of Radiance, etc), names, etc.,...I have no problem creating my own.

The only thing that matters to me: the game/story has to be "good" - it really doesn't matter, in which way the characters are created.
As long as the story works with the characters available - all is fine.

Edit: wording

Pre-made is basically a requirement for character-related story arcs and personalities and for actually caring about the characters, as characters as opposed to a sum of stats. And since I want that in the games I play, I also prefer this option. But that does mean that those aspects better be good.
If the focus of the game is just the combat (or otherwise actual gameplay), not story and characters, then obviously custom. Forcing premade characters that will still end up being seen as a sum of stats is the worst of both worlds.

I have no real preference, but if I were forced to use a party, I'd want a game to allow me to use custom made characters. Of course, that all depends on how the game's narrative is presented as well as the quality of the narrative.

Depends on the game. Games with lots of lore, story, plot, background, dialog, history, NPC conversations with ways to influence them... companions with background.

Hack and slash game that's primarily combat with no depth to it... make my own.

Ideally though, I'm more in favor of solo games over party. Solo games offer more challenge IMO by giving you a character with strengths and weaknesses, and it's up to the player to handle it, as opposed to a party that can cover all necessary skills. What's more, a solo game is more immersive and intense when I'm only having to fight, or hide, or stealth, or magic, or whatever with only one guy, and don't have to worry about leaving others behind or what to do when some members fall.

2 with a mix of 1, like FF5. Premade destiny, customizable in every way.

What I've always thought would be good would be something like the Origin system from Dragon Age 1 or Divinity OS2, but applied to the whole party.

So you'd create 3-4 characters, and pick a backstory for each of them, and that backstory would then give them an in-game personality, party chats, NPCs who know them, sidequests etc. Ideally, different combinations of class/race/origin would result in entirely different characters too, so an elven mage war hero would be a different experience to having a human fighter war hero in your party.

You'd probably have to do away with voice acting though. Not a problem for me- I actually prefer RPGs unvoiced (or at least, with only battle 'barks' rather than fully voiced dialogue), but might be a sticking point for some people.

I prefer those party-based RPGs that let you create one or two characters form the start and then you can find during play other people to become members of your team. For example Drakensang: The Dark Eye or Divinity: Original Sin. And not have them created or given to you right from the start. I find it overwhelming and confusing. So no Temple of Elemental Evil or Icewind Dale games for me.

Also, I don't like so heavy-text games. What little time I have I want to play/explore/kill/solve quests, not read! So no Baldur's Gate games or Pillars games for me either.

I think Drakensang: The Dark Eye and Divinity: Original Sin 1 had the perfect balance. I haven't played DOS 2 yet, but I will. To my mind the more reading it features (than DOS 1) is counteracted by the fact that it's fully voiced, so others read it for you! Also, I wish for GOG to bring the other Drakensang game as well.

Pre-made party members with entirely player-made customizable main character.

In which category you would put The Darkest Dungeon?

I'm not actually familiar with that game.