Both Gondor and Rohan are very European in their styles. Rohan's weapons are very much inspired by Celtic swords, and Aragorn's sword is pretty much a German bastard sword.
Yes, which is why I said that the "Elven" swords didn't look European, with the exceptions of Sting and Glamdring.
For the record, Rohan's material culture is Anglo-Saxon/Vendel, not Celtic. Aragorn's sword is late Medieval in inspiration, presumably because that allows it to be bigger and more impressive than everyone else's, which is a decision I find unimaginative.
That's extremely subtle for a movie though. I for one LOVE the design aesthetic for each race. Why would two completely different cultures/races make the same style sword or axe? It's like saying the Chinese and the Persians should both have used shamshirs, because a "sword is just a sword" (which it never is)
But that's precisely the point I seek to make: I don't think Tolkien intended the "good peoples" of Middle Earth to be that culturally alien to each other, because they all stress different aspects of Northern European language and culture. The Rohirrim speak a version of Old English, the Elves speak a version of Welsh (Quenya) or Finnish (Sindarin), and the Dwarves speak a variation of Old Norse. The material culture of these historic peoples varied little: they fought with swords, spears and axes that looked much alike, wearing mail and helmets that looked similar, carrying round wooden shields that shared a basic design.
Remember that Tolkien intended Middle Earth to represent an invented mythology for England. It follows, I think, that their material culture of its inhabitents should be drawn from the Northern European environment of which England was a part. That means straight swords and chainmail, not curved scimitars and scale armour.
Remember that Tolkien didn't pull "Elves" or "Dwarves" out of the air: there was a time when people believed in these beings. Certainly, they were considered to be strange and probably magical and different from ordinary men and women; but would a pagan Saxon in 609 AD really think of them as "foreign"? I think not. I think they would have been perceived as a hidden and ancient aspect of their own culture; just how leprechauns are seen in Ireland.
This is borne out by the fact that the only straight bladed Elvish weapons we see are Sting and Glamdring. Why? Because they are used by Bilbo/Frodo and Gandalf, who both clearly belong to the European style human culture, and the production team realised it would seem incongruous to have them use Asiatic-style Elven weapons. So these two Elven swords are conveniently totally different in design to all the others.
They have tried to go half way with Thorin's sword, and turn into a single-edged falchion type thing. It is the only sword of its type in any of the movies, which is silly.
I personally don't see it. What about them says samurai to you?
When at leisure, the Elves wear flowing
kamishimo type robes, with high "Nehru" collars. When at war, they fight with Asiatic composite bows and
Naginata- watch the prologue of FOTR in particular. The scale mail has a Persian origin, but the cultural influences are all from either south of the Mediterranean or east of the Steppes. That culturally aligns the Elves with the Easterlings and Haradrim, not the Men or Dwarves with whom they share a millennia-long history of alliances and cultural interaction.
Let me stress that I do understand why the decision was made to make the "races" all culturally separate, and Weta certainly made an impressive effort to realise their objective. But I don't think it is what JRR T intended, and it throws up problems when you have to have Gandalf using a sword that looks like Gandalf's sword, and therefore eccentric in the context of its Elven typology.