High Magic is the purest and most powerful of all sorceries. For this reason a Mage with High Magic spells is always considered to be of higher magic level than other wizards when casting spells. Other types of wizards will therefore require a basic 5+ to dispel using a counter magic card.
When High Magic-using Mages confront each other, the normal ranking applies.
Note that this superiority only applies when casting spells, not when using counter magic. When using counter magic the normal ranking applies.