ha yea those names seem pretty backwards. Most of my damage is done with pyromancy, that's why I'm leveling INT, so maybe it would be smart to go enchanted incase I come across a fire-resistant boss?
If the majority of your damage is pyromancy, then I would personally go Magic (Faintstone) on the weapon, especially if you intend to keep raising Int (I assume to at least 40 or 50).
This is how it works (using Lucatiel's Greatsword as an example):
Base weapon (stat scaling is gonna be listed as STR/DEX/INT):
C/A/- 250 physical damage
Enchanted weapon:
E/D/C 250 physical damage
Magic weapon:
D/B/B 175 physical damage + 175 magical damage
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As you can see, Enchanted weapon doesn't actually add magical damage. It's all still physical. You just get to add Int scaling onto the weapon. The downside is it's pretty weak scaling, and it downgrades the STR/DEX scaling of the weapon by quite a lot.
Magic weapon splits your weapon into two damage types, which could be bad if you come across something that resists magic, but then you still have your pyromancy.
The upsides to this are:
A. You can see that the scaling is way higher, including the scaling it adds for Int.
B. If you ever choose to use Crystal Magic Weapon, the way the spell works is it adds a flat 50 damage to your weapon PLUS 30% of the weapon's magical damage value. This means that an Enchanted weapon would only get +50 damage, whereas (using the weapon above as an example) Magic weapon would get
50 + [.30 * (175+<extra magical damage you're getting from your int scaling>)].
So even without the scaling, the benefit would be 50 + 52.5
Any way, tl;dr:
Magic has higher scaling overall and splits weapon damage between physical and magic.
Enchanted has terrible stat scaling but lets you keep all of the weapon damage as physical plus getting to scale with int a bit as well.