Well, there's the fact that he's a very honorable guy. If he's a backslider in DmC, that'll basically be a change towards the core of his character which is bad if NT wants to keep the "spirit" of his character. That, and his power- lust, which I think is okay to change since that made him a rather confusing character. Then there's his coldness, which is also something that I feel is okay to change since that also made him rather confusing.
I think that, if they kept his calculatory attitude and honorable nature like they did with Dante's cockiness and over- the- top style, they wouldn't have as much backlash as Dante initially got.
(By the way, as a side question, does anyone know why Itsuno decided to give Dante an over- the- top style of fighting? DMC 1 Dante's fighting style was pretty straightforward.)