Well, of course Character Attack influences all elements, the name already hints at it.

With character Attack you increase the Characters Attack (their Base stat, like Assault does it). This is completly unrelated to the elements of your attacks, since they are not relevent when it comes to character attack.

Elemental on the other hand has nothing to do with the characters attack stat, it only influences a specific element, though of course on Solomon's Ring, it will influence only that specific hit while your character attack influences the whole attack, every hit.

That's why character Attack has a much higher influences then elemental attack, unless it is "All Elements" like Vlad does it.