Char atk is assault - same as assault weapons, atk is elemental - same as offensive soul weapon. People often then ask which one is better, so let me preemptively cover that, too by showing the simplified damage formula:
Dmg = base atk * (1 + assault) * (1 + elemental) * (1 + special atk) * bunch of other stuff that
I am assuming you don't own a 100%+ eidolon, 'cos if you do, just use that and dun need to read the rest of this post.
- When you're first starting out, and have not slvl your weapons yet, assault and elemental are the same - pick whichever one gives you the highest number.
- When you've slvl a bunch of assault weapon, assault value tends to far exceed elemental, in which case elemental eidolons are usually better.
- When you have a maxed out elemental atk soul weapon and you have 100% eido support (friend or not, doesn't matter), char atk eidolons can be better.
- During UE, grail buffs are assault, so elemental eidolons are typically best then.
tl;dr - for char atk vs elemental atk, pick the one you have less of.
Note about Lilim: her char atk only applies if you have 3 different elements on your main team (subs dun count.) So if someone dies and you no longer have 3 different elements, you get zero bonus from her.