Its a good question, but not one with an easy answer.
Speaking as a DA2 detractor, I think there were a number of things wrong with the game. Speaking with my general gamer hat on, most games have things 'wrong' with them that could be improved.
Does the distinction matter? Yes. I've yet to come across a fan or a detractor that was happy with the reused environments, that didn't express some form of grumble relating to the dialogue wheel, who wouldn't have preferred choices to have greater consequences and who would have liked the game to be a bit more seamless and true to the original idea rather than the slightly more choppy and rushed end product we got.
Most of us would like the return of racial choices (although we differ on how much we would be willing to sacrifice to get this, and whether its conditional on races having a meaningful difference on NPC reactions and storyline), and we all seem broadly positive about the proposal to make classes more meaningful in terms of NPC reactions. I think we'd all have liked to get out of Kirkwall a bit more, or at least see the city change and develop over its 10 years.
So those aren't the things that got the DA2 detractors frothing at the mouth. They just added insult to injury.
What's more interesting is where the fans and detractors tend to violently disagree. Because at this point, what I've seen is a lot more general grumbles about the change in direction.
There's definitely not universal agreement amongst detractors (or amongst fans, for that matter), but common topics I've seen set the BSN against itself are things like;
The focus on the Mage/Templar war
The aesthetic resdesigns (races, armour, weapons),
The UI redesigns (quest markers, codex, amount of 'handholding' given to players)
The voiced PC (including the linked changes to dialogue display, dialogue icons and feel of character ownership) The shift towards more cinematic and (over)dramatic storytelling,
The changes to combat style and epicness (e.g. combat speed, exploding bodies, teleporting rogues),
The changes to combat balance (e.g. superpowered PC abilities versus trash enemies leading to wave combat and HP-bloated bosses and lieutenants to retain difficulty)
These aren't as fixable, because they have a huge impact on the overall style and feel of the game. And that, I think, is the common factor. The divisions are about how it was designed to play, look and feel...and what its priorities were in delivering to the audience.
DA:O was from the same design style and vision as Baldur's Gate and Knights of the Old Republic. It appealed to players who enjoyed the features and appeal those games brought, and for the strength of its storytelling.
DA2 was far closer to the design style and vision as Mass Effect and Jade Empire. It appealed to players who enjoyed the features and appeal more common to those games, and for the strength of its storytelling. Oh, and it was poorly executed in comparison to past titles.
DA and ME have demonstrably different fan bases, albeit with a clear element of overlap. But not everyone actually values the DA2 / ME / JE styles and design priorities.
To switch between them mid-series must have looked great on paper as a strategy (Game of the Year RPG takes on elements that made Mass Effect our best-selling series to date, whilst not becoming Dragon Effect), but was an incredibly brave (stupid?) move that predictably tore a socking great hole in the DA fanbase.
"Fixing" that might require a genuinely significant rethink about who the DA series is designed to appeal to and what that means might have been changed in error. Or the poor feedback might be pinned primarily on execution errors, and the DA2 model will be given another go with DA3...which I think is more likely.