We've finally nailed down two issues, which I call D&D's "American" problem.
eh... its not so much American as it is just D&D. There are plenty of American games that avoid these issues. Some of them are even D&D spin offs.
1. D&D defines your character through your job (primarily)
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1. What do you start with in D&D? Well, technically stats - which is worse - but primarily your job (class). Your job tells you what you can do, and you can do nothing else. 5.0 expands this to your 2nd job (background), which is good, but what we like about some other systems is that you start with your personality, and ...well you never really define your job. You have abilities / powers, but those are means to an end: not the definition of what you do. Your personality defines your character traits, not your power palette or balanced party role.
Mmmm.... a few things to keep in mind about all of this. Vampire, both Masquerade and Requiem, are renowned for their focus on the Social aspect of gaming. So, when you're comparing D&D to the WoD, you have to keep that in mind - the two games are pretty much designed with a different focus between them. Social interaction versus combat.
Secondly, others have stated that clans and classes do have similarities. They're both archetypes that help shape a character's direction. In fact, clan determines your role in vampire society when they come prepackaged with a philosophy you're supposed to follow - its something that many people have griped about the game, but live with it.
Three, the games have vastly different methods of leveling. Would a point system that allows you to take Fighter abilities at an XP penalty despite being a wizard solve part of this issue? This creates a more organic style of progression, as opposed to the railroad track of 1-20 levels that D&D currently use (and is effectively a sacred cow).
From reading your responces here and throughout the thread, I'm coming to the conclusion that what you are asking for isn't quite as clear cut - it feels like there's something missing in D&D that you like elsewhere, but I don't think its merely the point at which you work on a character personality. If it was, then the answer to your question would be "start by figuring out your Flaws, Ideals, and Bonds first, then the rest of your character." And I somehow don't think that's the answer here - moving around the order of character creation somehow seems like it won't solve the issue. Could you go further into depth about what exactly that's bothering you about the class system? Is it immediately at character creation, is it as you grow up, is it merely the archetypes that you have, is it the feeling of being locked into an archetype with no escape?
What vampire clan is a Cleric?
Salubri. Hands down, the Salubri, with a side of Losombra in place of the evil cleric using necrotic energy. I know, I know, Obtenebration really feels more like a Shadow Sorcerer thing, but the whole religious bent of the clan makes me feel that they should get at least an honorable mention here. As for the rogue? Aasimites and Ravnos (well, assassin and arcane trickster, but close enough). Daughters of Cacaphony are the bards.
2. All actions in D&D result in 100% success or 0% failure (no moderation)
2. In combat, you hit or you miss. If you are trying to convince someone or climb a wall, it's the same principle: a static DC - a number that defines whether or not you succeed or fail. Casting spells means they either 100% happen exactly like you thought - or you are out of [spell resource] and they do not happen at all. Everything is binary, which is secretly the least "realistic" thing about D&D. Other systems that we like use degrees of success: you can fail, fail badly, scrape by, succeed a little, succeed, succeed a lot, impressively succeed, or succeed beyond your wildest expectations (to name a few). (D&D has crit successes [and you can add crit fails] but those are only combat rules and still basically binary.)
I'm personally of the opinion that the three pillars of D&D (exploration, social interaction, combat) should actually be four - I call this the Building pillar, with a focus on things like followers, strongholds/lairs/dungeons, creating works of magic, etc. And I feel that this applies to almost any game out there as part of the design of RPGs.
However, when you look through the books? The overwhelming majority of mechanics are strictly based on combat. And, yes, combat has more than just a binary system. Hitting alone is botch, miss, hit, nat-20, which, by definition, is not binary. You miss, you mess up so badly you cause problems, you hit, you strike a vital spot. And then, we have things like amount of damage taken, status effects, initiative, positioning/sneak attack stuff, and the like. Combat is really complex and involved. Outside of combat is entirely defined by the skill system - Exploration/investigation, social interaction, and building things of all sort are handled by that binary pass/fail.
The problem here isn't so much that the game is binary, the problem lies with the skill system. Its too simple. There are a lot of games out there that have more complex systems that are actively engaging. And they have a direct effect upon how players think and act within the game. When D&D treats "beating" a diplomat check in the same way you handle beating someone in a race, it creates a certain mindset. Either I'm good and everyone falls to me, or I miss.
Others have suggested multiple rolls, but that's really just touching on the tip of the problem-iceburg. The fundamental problem here is that exploration and socializing are complex affairs that tend to be handwaved away and over simplified, to the point that you have to determine your character's success through describing actions more than doing anything with dice or what a character should have as an ability as opposed to the player's ability.