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In the rulebook it says you can have an elf with armour, elf bow and elven blade while this is a galadhrim warrior with an elven blade and bow but galadhrim may only have one of these:elf bow, spear,elven blade.
Just because they have the same equipment doesn't mean they are the same model (although it's a little confusing). As whafrog said, High Elves just have enormous flexibility. So yes, you can give them the exact same weapons as a Galadhrim warrior, but because they aren't actually Galadhrim the special rules about swapping the Elven blade for a spear, etc. don't apply.
It's very open ended, but that's because the High Elves have never really gotten an update (other than a few heroes in the Fall of the Necromancer) or a sourcebook of their own. The Galadhrim are more restricted because they have been recently updated... but the upside is that, even if slightly more restricted on their weapons choices, the Galadhrim have a thematic army list and more variety to choose from than the basic High Elf warrior from the main rulebook.