There isn't really. There are tons of fans that love both. You only really see the Witcher vs DA stuff on the BSN. That's because these boards are filled with Tumblrites always banging on about misogyny and objectification and racism and LGBT representation. The Witcher doesn't really cater to those people which is why as somebody else said, they throw mud at it and hope it sticks.
This.
So. much. this.
It is a lot like Marvel vs DC quite frankly. LOL.
But I will say that I like Witcher more than DA, especially these days. Why ?
The Witcher franchise is a lot like the Game of Thrones. By this I mean The Witcher makes no excuses about what it is. It does not pretend to cater to anyone, it does not push any agenda of any sort and most importantly, it adheres to its niche. CDPR does not give much of a damn if specific groups are offended by things in their game in the same way George R. R. Martin does not really give much of a f**k if people get offended by the incest, violence and what have you that is in his book. There is no inclusivity drive of any sort, no talk about catering to one demographic because sexism, representation, etc. CDPR just makes their game and that's it. No social justice nonsense.
Bioware is not like this. Not even remotely. They neutered, diluted and dumbed down the dark and grit that was in Dragon Age Origins to the generic fantasy that is Dragon Age Inquisition. They do not stick to their niche and instead just copy and past features from other game franchises. They try this balancing act, trying to cater to everyone which ultimately fails. I mean, what happened to desire demons ? Or brothels ? Or equal romance content ? Or tactical combat ? Or things such as sexism in Qunari culture which was conveniently whitewashed away ?
As for the fetch quests, it was poorly done in DAI. Bioware decided to copy Skyrim's approach to side quests and this ultimately fails because Skyrim is a sandbox RPG, not a tight story driven RPG. This "fetch X amount of meat" is so similar to "fetch X amount of atronach salts and deathbells". They decided to flood the game with pointless side quests while relegating lore to minor quests which are either difficult to notice or takes place on the War Table, which again is very reminiscent of how Skyrim does it with their scattering of books and side quests in the remote corner of the world somewhere.
Bottom line, the side quests in DAI are the way they are because Bioware lost touch with their niche. They forgot what Dragon Age as a franchise is and instead just decided to blatantly implement features from other popular but dissimilar games (that whole scanning crap ? Taken right out from Witcher 2 and many hated it in Witcher 2) because profit$$$....