It is kind of funny that Archer's Lifting Class in his weaker Key so happens to be the same as Roxas's. Anyways, I'll lay out some Advantages and Disadvantages as I can see for each fighter. And just a note; Due to the page for No Name stating him as formerly being Shirou, he should scale to his skill for the most part.
Archer:
- Vastly Superior Lifting Strength
- Precog
- Servant Physiology
- Has far more weapons at his disposal which he could either pull out and use personally or throw at Roxas in a Danmaku Style from UBW, each weapon being a Noble Phantasm and usually having somesort of extra effects attached to them.
- Amazing Information Analysis and Power/Skill Assessment (As seen in the Skill Feats linked above; Even a Shirou Emiya prior to gaining any power or skill could analyze Servants Skill's and Power's in comparison to one another accurately.)
- Is likely to change up his strategy if it isn't working; If fighting Roxas with Swordplay is ineffective, he may switch to using a Bow. If that fails, he may bring out UBW to spam relentless attacks. Etc.
I can't, think of any notable disadvantage's personally to be honest.
Roxas:
- Vastly superior Range w/ things like Magic
- Nobody Physiology
- The Keyblade. Nuff said.
- Info Analysis which can allow him to see Archer's Health
- Can be aggressive and careless in battle
- Unless we take Sora's skill into consideration, while Roxas is skilled, he isn't as versatile in terms of weapon's, and unlike Sora we don't really see Roxas stealing weapon's from his opponents (Unless he's taking them back from someone like Sora; Even then, in Day's he doesn't even bother trying to take back Oblivion from Riku until the fight is practically over already, and he can use Magical attack's barehanded, so it's clearly never the first thing in his mind even when his weapons are taken from him.)
So, I can see a few Wincondition's. Archer's main wincondition's would be throwing around his LS to subdue Roxas (Though this isn't exactly in character to my knowledge), and Abusing his Weapon Spam to try and overwhelm Roxas. He can also use his Precog and Analysis to better deal with Roxas's own attack's.
Roxas's best wincon would be to build distance and then outrange Archer with magic, but this isn't very in character for him- In fact, there are fights where he doesn't even use conventional magic much at all (Like in KH2, where he only uses magic to mainly supplement his melee strikes). Roxas is actually much more likely to force a close range fight than Archer is, who would be more willing to build distance and attack the opponent from a range if it is beneficial, so I don't see this happening most of the time.
Of note is that Archer has ways at his disposal to read Roxas as well as predict his next move, which Roxas's aggressive battle style might make even easier potentially. I'm personally leaning a bit more towards Archer here, though I see this fight likely turning into a battle of attrition; It's simply the fact that I could find more advantages that could prove relevant to the fight for Archer than I could Roxas, as while Roxas's range advantage is notable and could be a very easy wincon, Roxas just isn't likely to use it that much from what I know.
Of course, I most likely may have missed a few things, so I'm open for changing my mind, that's just what I see from the available sources about the two and what I determine based off that. I also definitely didn't comb through every single ability on both pages to be entirely honest, I just picked out what I could recall and what stood out to me, so there could be something big on one page the other just has no answer to, though I don't think there is.
