All fair points, this is why I wanted to talk about this match because I think there's a lot going for both parties. This is sort of like the Schrodinger's Cat of battles, both fighters are in a state of victory and defeat until observed. Some of my points rely on assumptions that there's not an easy answer for, and others weren't explained clearly. Also, I neglected to bring up the specifics of Dante's arsenal that Kratos will have a hard time counters, which is a factor I think is getting a bit over looked.
Blocking - Fleece vs Royal Guard
Honestly, this is a tie. Much like Devil Trigger vs Rage mode, they're practically one in the same. Dante can block anything with his Royal Guard, and Kratos can block anything with his fleece. The only difference is, if I remember correctly, Kratos can stand to block any incoming attacks and if he instead times the block at the moment of impact he can send the attack back. Meanwhile Royal Guard is all about timing, but every attack gets stored to be unleashed as a wave of energy or converted to either heal Dante (in addition to his healing factor, probably a late game trick he can pull out - which, healing would also help restore some speed to his healing factor) or turn him into Drednaught and start the "Invincible mode vs Invincible mode" debate. I'll admit I could be mistake about if Kratos has to time his block perfectly to "return to sender". But, if he does, there's only a couple tie breaking questions. What attacks are too fast for Dante to block? In my mind, nothing short of a sneak attack. While Royal Guard was too difficult for me to master, to the point where I stuck with the other styles, this isn't a Dante controlled by me. Instead, Dante and Kratos are at peak ability. I'm not going to restate Dante's speed feats, but I think he's quick enough to even react to the lightening attacks and can be used to block multiple incoming attacks (if your quick enough with the button, which isn't a factor here). I also think this guarding ability applies to any area attacks that both fighters can throw out. The other question, what can Kratos throw back and what can he throw back effectively? I know that Kratos has had explosive projectiles thrown at him which he through back, but those seem to be timed explosions. He catches the fireball, throws it back, then it explodes. With the missiles, if he catches them, they explode and there's nothing to throw back (maybe he can throw the fire back, but it's not really a solid mass anymore). I'll assume Kratos is capable of blocking and throwing back bullets, under the right circumstances, but they won't be nearly as fast or dangerous as the one's Dante fires, and he won't be able to do so with every, or even most, shots. I think the issue with my understanding is trying to figure out where game play mechanics begin and end, since some aspects of both player's weapons and abilities are limited for sake of game play and others are enhanced for sake of game play. So I think the only things Kratos can reliably send back are Dante's energy based attacks, or attacks where he throws his sword. Tie that is with finding a happy medium that works for both players and we create all these loose ends.
Area Attacks - Lightning, Rocks, Missiles!
Am I missing any attacks when I say Krato's area attacks are the Atlas Quake, Poseidon Rage, Army of Sparda, and the Medusa Flash freeze? If so let me. Again, blocking is an option for both parties when discussing any attack thrown, so from here on out I'm only talking about other viable options. My Poseidon's Rage vs Alastor DT theory is, assuming that switching between weapons for both parties is as simple as in the games (instantaneous) and activating DT/Rage mode is also instantaneous, then as soon as Dante sees the lightning he can activate the counter. And, making another assumption, that Dante doesn't need to move to pull this off, he can even activate mid attack - weather he would have the presence of mind to pull it off is up for debate. But I liken it to combat instincts, since Dante is no stranger to electrical enemies; like a marine being able to fight through a bullet wound. It's true that Atlas's quake sends boulders flying, but Jumping does not render Dante hepless against projectiles like it would someone else. Dante's quick enough to jump off of them. Strong enough to catch them. His bullets can stop them if he rapid fires (https://youtu.be/QWWoNkyRYY0?t=1m31s). Ironically, that scene shows Dante not doing super great against lightening, but it does take place before he gets a hold of Alastor. And his sword is strong enough to deflect them. Also, Royal Guard can be used in the air. I did neglect to acknowledge the flash freeze aspect of the Medusa Gaze, I meant to say something about it by I forgot while writing my response. Basically, that's what my point of Dante knowing what the head would do was meant to address. If, Dante doesn't know what to do then this point is invalid, but given his line of work I feel that's a safe assumption. The moment that Kratos grabs the head, Dante will see it and react accordingly. Before Kratos can utilize the stare, either the flash or standard version, he'll either put a bullet through it or Kratos's hand to try and make him drop it. Another thought I just had, and I'm raising it more as a question than as a point. Kratos can break out of the stone, allowing him to escape being smashed to pieces. I assume the same goes for Dante, but Kratos won't hesitate. Kratos smashing the stone Dante would certainly kill him. So, my question is, could Dante speed out the break-out process by activating his Devil Trigger? He'd presumably get hit still, but chances are it wouldn't be a killing blow. Again, this is the sort of fight where that could lead to a killing blow, but it could also give Dante a chance to counter attack. But Dante has area attacks of his own, or at least attack that achieve the same goal. And up until just this point, I thought that Dante had more going for him in that area than he actually does, because I can only actually think of two.
www.youtube.com/watch?v=oz54vJsftuc the PF594: Argument isn't exactly an area attack, but in a one on one fight it might as well be, since it can fire 14 homing missiles that attack from various directions. The other attack the PF666: Omen, the first move shown here
www.youtube.com/watch?v=xo-fZZGgU8k, just straight up kills anything in front of it. Granted, Kratos is stronger than most enemies that Dante encountered with his demonic briefcase, so it won't kill him outright but it will do massive damage. And, much like how Dante can block Kratos's area attacks, Kratos can block these. But if any of them hit, Kratos will more than feel it.
Speed Boost - Reacting and Running.
Honestly, I could be mistaken and forgetting a cut scene but I don't remember there being any indication that Kratos has much of an ability to react when using the Boots of Hermes. I just remember running in a straight line and mowing over enemies. This can be used to effectively close the distance and possible get a hold of Dante, especially if he doesn't see it coming. And if Kratos has his hands on Dante, he could easily grab him by the neck and stab him stomach over and over until he stops healing. But, Dante's counters for this include Quicksilver - slowing down time to put the speed advantage back in his favor, and his Trickster abilities - with Air trick allowing him to vanish and reappear, moving at least the speed of Kratos in the boots, just over a shorter distance. Still, if he times his Air Trick right, it would be enough. Still, weather or not Kratos gets the appropriate reaction boost, Dante has his Gilgamesh to increase his speed and strength
www.youtube.com/watch?v=ZKOfilDf5G4. This not only puts speed back in his favor, but at the very least closes the gap in strength.
Rage - Dante is annoying.
Do not sell Dante short, I think he is way more annoying than Hermes. We're talking at least MCU Tony Stark levels of obnoxious banter. It's his number 1 skill. Now, I'm not suggesting this will make Kratos go all out and become a mindless beast. I'm just suggesting he'll get mad and throw an ill timed attacked. In a fight like this, that's all it might take for either side to win - one really good opening. Your point of Kratos going Rage mode is fair though, and brings us back to the Schrodinger's death match aspect of this battle.
Healing - Time heals all wounds.
I was very unclear on this point and worded that terribly. In general, we're talking hours of combat to lower Dante's healing powers significantly. After two back to back boss battles, including one being against Vergil, Dante was still able to heal rapidly in Devil May Cry 3, when he was at his weakest. Kratos will speed this process up. But, due to blood replenishing, Dante's healing factor speeds up as he heals. Making it really hard to tell how much it takes to effectively slow it down. This fight could last minutes if Kratos lands all the big attacks he needs, it could go hours if Dante manages to dodge and block enough, or it can be over instantly if Kratos thinks he just needs to stab Dante, because it would leave him open to a close range counter attack. It's the kind of advantage that edges this match in Dante's favor for me, since this is the sort of fight that usually comes down to who lands the killing blow first - in this case Dante can win if he lands it first, or second.
Claws of Hades - We are the sons of Sparda, and within each of us flows his blood, but more importantly, his SOUL!
All I have here is that, yeah, Kratos could rip his soul out. I sort of forgot about that ability. While Dante's power is literally in his blood, his often attributes it to having a soul, "First I whip it out. Then I thrust it. With great force! Every angle..! It penetrates! Until..! With great strength! I.. ram it in! In the end, we are all satisfied, and you are set free." Wait, no, that's the wrong quote. Here's a better example,
youtu.be/bw8UswJlo68?t=1m37s. So, yeah, if Kratos rips his soul out game over. I do think Kratos's chained weapons are the perfect thing for Dante to counter though.