It depends on my mood. No, really, sometimes I want the "my story, my decisions" gameplay, but sometimes I just want to enjoy a good story that happens to be interactive. Or sometimes something in between. So I'll try to explain what I expect from the two extremes.
An open-ended character creation is important in the first option, of course. In the context of Dragon Age, maybe you want to be a human commoner. Or heck, an Orlesian elf servant. Games that cater to this would be the Elder Scrolls and Icewind Dale series. They're good series, but more often than not, I get that "being-farted-from-the-primordial-soup" feeling about the character. They just suddenly come into existence. There's nothing from their backstory you can interact with, nor the game acknowledging that you have said backstory. In contrast, I've played PnP games where as part of the campaign, the DM would craft a character-specific sidequest for each PC and his/her background. This, in part, simply comes from the limitation of the medium. A pre-written, pre-programmed CRPG simply cannot handle the infinite possibilities of different character concepts, which is why I won't fault them for failing to meet these expectations.
So we have to accept that it is in the nature of CRPG to either have limitations over your character's background (Dragon Age and Mass Effect) or simply skirt around mentioning anything about it (Elder Scrolls). Which one you prefer would obviously be a matter of preference.
Now the other extreme. This one is easier to implement in video games. We have seen the Origin stories in Dragon Age, which is a form of limitation (although perhaps more akin to Choose Your Own Adventure book genre). We have also seen it being pushed more in Dragon Age II, where we're always going to be Hawke. Mass Effect takes the middle approach where your origin isn't playable, but is acknowledged in-game. For me, I can dig all options equally, with the main caveat that the story itself is well-written.
So what about Hawke, essentially the extreme of extremes? I can't believe I'm going to do this, but I'll compare Hawke to Bella from Twilight. Both characters have preset, with some guidelines to their personalities and backgrounds, but both are still vague enough so that players/readers can inject themselves into these characters. In Bella's case, her personality is tailored to be bland for this specific purpose. In Hawke's case, Bioware opted that we can pursue three archetypal characteristics rather than generic blandness (and here I suggest is why I don't like the Elder Scrolls series all that much, the characters are simply too bland). Namely: goody-two-shoes, deadpan snarker, and jerkass. This decision, of course, is probably informed because they wanted Hawke to be voiced. In my opinion, this suffices; I can roleplay within these confines to create "my" Hawke. Rogue!Hawke got the snarky personality and generally wants to protect his sister. He sided with the mages. In contrast, Warrior!Hawke is a jerkass and actually resents having a non-life to protect a mage sister who's more of a burden. He sided with the Templars.
I like Dragon Age II. The story is excellent and the characters are interesting (even more so than Origins; I never thought that would be possible). The pacing does get uneven in the middle, but I get all the foreshadowing so I thought all acts are important and fascinating.
So, moving on to Inquisition. I personally love the way the main character is handled in Mass Effect. Not only does it provide sufficiently diverse character backgrounds to choose from, it also allows voice-overs in an economic manner. Taking into account that this is a computer game, and thus everything has to be pre-crafted, I don't mind not having many choices in character creation as long as I can be enraptured in the narrative. All that needs to happen for that is that my in-game choices (that is, ones made *once* I have that pre-crafted character) to matter in some way. It doesn't even have to be major; we can't all be Forrest Gump, after all, but simply an acknowledgment from the game that yes, we know you made that choice.
After all, if I truly want to create my own story, I'd rather write a novel or go play PnP with a cooperative DM.