The original dodge mechanic was part of the things Devil May Cry needed to evolve. There's nothing impressive or smart by taking a mechanic some games can simply put down to one input to demand multiple ones. It's just unnecessary. The same with how moves were locked away from you unless you lock on. DmC went around some of these things bringing some of these techniques to a natural and much needed evolution. The result is a concept that gets mixed results, but was at least had well intentions.
As I will now explain.
DmC puts many different variations on things all throughout combat. The dodging mechanics in it are no different. There are actually THREE variations of the dodge. Demon, Angel, and Nephilim.
-Demon Dodge: This evades enemy attacks while delivering a boost in strength on the next attack.
-Angel Dodge: A quick dodge that allows you to travel further distances via teleport
-Nephilim Dodge: This is activated during the Demon Dodge and you have to time it properly. When Dante goes in slo mo, you can notice his hands glow red which indicates the time to activate the Angel Dodge, this will allow you to have not only an attack boost, but the ability to travel that distance. A combination of both.
I see the intention in allowing the different perks, but there just isn't enough to really garner it as a necessity since most people just use it to dodge attacks.
If it were up to me, I'd have added more reason to perform these dodges. It needs a better argument to justify its existence. Like, for example, with the demon dodge, not only would I have allowed an attack boost, but the ability to use the Arbiter's Tremor technique which has the fault line separate in to three different directions instead of one straight down the middle. Or maybe the Eryx has this move that successfully performing Demon Dodge allows. A barrage of punches that Dante delivers to nearby demons. Like a 3-hit boxing combo. The repeated success of demon dodge would not only increase attack power, but add more hits to the combo.
Maybe a max combo of about 7 hits that is capped off with an instakill knockout punch with the demonic voice yelling KO! And maybe a bell ringing. All about style baby, all about style.
Do the same with Angel Dodge. Give it more perks an abilities. I could go in to explaining what I have in mind for an Angel dodge perk, but I won't unless you want me to.
The Nephillim Dodge if successfully performed could allow you to mix and match both with maybe a slight boost in speed. The chance to speed up the Demon Dodge perks if you so wish.
So, yea. It's something that has potential even if it's assigned to two buttons, but there is room for improvement and it doesn't have to be so arbitrary to perform.