For that to be the case, they would have to make the new wizard more complex than the old wizard, since right now the old fighter and the old wizard are close to being on par. (I suppose the old wizard is a little more complex, what with the spellbook, but it's a very minor difference.)
My experience is that the 4e fighter is significantly more complex than the 4e wizard, especially to explain to new players, because of the complexity of Combat Challenge and Combat Superiority.
In previous editions, the Fighter was the least complex character who was a very good introductory character choice. In 4e, it's pretty much the most complex (PHB1) character you can give someone. (The simplest is probably the ranger).
In actual fact, I consider this to be a failure of design. The two powers are also easily confused. Consider this:
* A monster moves away from the fighter, and the fighter can't attack it.
* A monster moves away from the fighter, and the fighter can attack it, but it doesn't stop moving. The fighter doesn't get a bonus to hit.
* A monster moves away from the fighter, and the fighter can attack it, and it stops moving if he hits. The fighter also gets a bonus to hit.
All three of those are true for the fighter, with slight variations depending on words like "Shift", "Move", "Opportunity Attack" and "Immediate Interrupt".
That is truly terrible design, and it is a blot on a lot of excellent work elsewhere in 4e design.