Thankfully, in our testing, both PS4 and Xbox One turned in excellent performance overall, delivering a smooth, stable 60fps for the vast majority of the duration. In fact, frame-rate on the whole is actually more consistent here than it was in its original console incarnation.
Unfortunately, for those interested in ramping up the experience to the next level, there is a caveat - there are slight performance issues on Xbox One when playing Legendary Dark Mode. This is an challenging gameplay mode previously introduced in the original PC version of the game that throws a much larger number of foes at the player. More than any other mode, this setting demands a perfect frame-rate - something that the Xbox One can't quite provide in all instances.
Essentially, we're looking at minor dips into the mid-50s - something that is just enough to interrupt fluidity. By comparison, these same sequences play without issue on PlayStation 4.
It should also be noted that a reasonable level of texture filtering is applied on both systems, unlike the initial release of DmC Devil May Cry on PS4 earlier this year.
As for which version to consider, it's pretty clear that the PC version comes out on top in terms of technical performance. Support for higher resolutions and hardware MSAA combine with excellent performance on a wide range of hardware to create a wonderfully polished experience from top to bottom - just don't plan on playing the game with a mouse and keyboard if you decide to go down that route.
Between the two console versions, it's easy to imagine that casual users would be happy either way since they both offer a nice improvement over the original release. That said, we have a real preference for the PlayStation 4 version due to flawless in-game performance in all modes and the more comfortable R1 and L1 buttons. Even considering these minor quibbles, Devil May Cry 4: Special Edition is perhaps the highest quality remaster Capcom has released this year - regardless of platform.