I like that definition, actually. Wizard's Constitution does reflect the biological differences in a wizard, especially when you consider how Butters explains Harry's "electromagnetic field."
In terms of mechanics, there are some benefits to being a full Wizard.
Straight off, you have an extra source of Fate Points from the added compels when dealing with modern technology, and compels related to the character's membership of the White Council (Harry makes it clear in YS that the only reason Elaine isn't forced to join is because she pretends to be weaker than she is, so it follows that anyone fitting the Wizard template must either be a member, or be hiding their true nature).
You also get to buy more levels of Refinement, which is the major way for magic-users to become more powerful. As blackstaff67 said, only a Wizard can buy more than two levels of Refinement, so over the course of a campaign, even a tricked-out Sorcerer with high Lore, Conviction and Discipline isn't going to be a match, magically-speaking, for a Wizard with the same amount of Milestones under his belt.
And there's a lot to be said for The Sight. It can be incredibly useful as an investigative tool.