Gameplay mechanics are, first of all, completely irrelevent, and the Protomateria is not a gameplay mechanic. It's directly referred to in the storyline, which means that it's not "just another powerup". Rather, it's a powerup that, according to in-game canon, Vincent has at his disposal. Whether or not we see it as "plot-relevant" makes a huge difference, mainly because items and powerups mentioned in the plot are canon, whereas those not mentioned in the plot (or in any official sources) are not canon. For example, Mako enhancements are canon to the storyline and are canonically at Cloud's disposal, whereas a mastered Knights of the Round materia is not canon to the storyline because it was never even mentioned in the storyline. The Protomateria is one such storyline item. Vincent canonically received it, and he canonically had it at his disposal. By that logic, I should be able to say that Mako and J-Cell enhancements are "just another powerup" for Cloud.

Besides, whether you take into consideration the Protomateria or not, Vincent has displayed the ability to use Chaos on-command, or at least in situations where he's not in any immediate danger. To say the least, he can use it MUCH quicker than Cloud can use Omnislash.

It doesn't matter if we see Protomateria in the story. We see Cloud's party members. How about Barret and Cid are fighting with him? The protomateria is an enhancement, just like any other materia, and is not an actual part if his body. That they can use their swords or guns, and wear a bit of armour is a given, but any enhancement beyond that is a handicap. We see materia in story sequences, omnislash and limits, too. Maybe Cloud already has this "Spirit Energy". It's just another enhancement, and while Zidane can trance naturally, or Terra can morph naturally, but the protomateria should be filed under an enhancement, just like starting with the "Spirit Energy" to use OmniSlash.

The Protomateria may be an enhancement, but it's an enhancement that Vincent has at his disposal and can readily use at any given moment to turn into Chaos. The Protomateria is no more an "enhancement" than Cloud's sword or Vincent's gun. It's a piece of equipment that, according to the storyline, Vincent canonically has. It's different from other, regular Materia in the sense that we see Vincent receive it, we know exactly what it does, and we know that Vincent can use it whenever he pleases. It's nothing like the Spirit Energy needed to use Omnislash because we know for a fact that Vincent can use it at any given moment. We've seen it, just like we've seen Cloud taking hours upon hours to build up the Spirit Energy for an Omnislash. Hell, Spirit Energy isn't even an enhancement, it's just something that needs to be accumulated over the course of the battle. However, Vincent can bypass that because he was given the Protomateria. It is an item exclusive to Vincent. We know that Vincent has the Protomateria at his disposal, so based on that, we know that he can use Chaos whenever he wants to.

Yet Vincent does not have the protomateria from start to finish. I can understand Cloud's sword, and Vincent's gun, but we rarely se ehim use the protomateria.

What difference does that make? We rarely see Cloud use Omnislash. In fact, there's only one canonical use of the technique on Cloud's part in the entirety of the compilation, and one canonical use of Omnislash v5 in Advent Children. By your logic, we shouldn't let Cloud have Omnislash. It doesn't matter at all when Vincent obtained the Protomateria. The point is that he did obtain it, meaning he has it at his disposal. In the same way that Cloud never uses Omnislash until the end of the movie/game, Sonic never turns into Super Sonic until it's time to fight the final boss, and Sora won't get Final Form until after he beats Roxas. Vincent has the Protomateria at his disposal. It doesn't matter at all how often we see him use it. The point is that we see him use it. It's something his character has in his possession that is at his disposal.

We see canonical use of materia, however, as well. Yet the debates are supposed to not include any of these enhancements tipping the scales.

Actually, I think Vincent would still win, because Cloud's only ever takena bulllet to the arm. Vincent could probably take him down with a shot to the heart or head.

Yes, we have seen canonical use of Materia, but we've never seen exactly which Materia Cloud has at his disposal, with the exceptions of I believe Thunder and Ice, which Cloud had at the beginning of the game and neither of which would be very useful against Chaos Vincent. The Protomateria is different from the vast majority of other Materia in that we know for a fact that Vincent has it, and that the powers it grants him are unique to him (or whoever is currently the host of Chaos, anyway). Whereas most Materia could easily be written off as not-necessarily-canon and mere gameplay mechanics, the Protomateria was visibly created within the confines of the storyline for the sole purpose of letting Vincent control Chaos and given to him directly. It's not another enhancement. We know that Cloud had some Materia, but we don't know which Materia he had, so we can't use them in this versus topic. Furthermore, any Materia collected over the course of the game (because I have no doubt that a large amount of Materia was collected) was the property of the entire team rather than exclusively Cloud's. The Protomateria, however, is one of Vincent's possessions. It belongs only to him, and we know for a fact that he has it.

However, without Chaos, Vincent would not win...or at least he doesn't have a very good chance of winning. It's true that a few bullets would do Cloud in, but the same can be said for pretty much every human in the Final Fantasy universe. By that logic, one good slash from Cloud's sword would easily kill Vincent. Under normal circumstances, guns>swords, but Cloud has shown himself capable of easily deflecting bullets. He even managed to deflect bullets from two quick/speedy opponents, so I doubt he would have much trouble closing the distance between himself and Vincent, considering he would only have one person to keep up with. Since Vincent specializes primarily in long-range combat or at least uses a long-range weapon, once Cloud manages to close the gap between the two, he shouldn't have much trouble offing Vincent. He's just never had much trouble with people using handguns.