[mike the snake]

I seem to remember the Audi Quattros totally dominating in road racing and in rally for years with their AWD systems.

Originally Posted by stugray

It is banned now, but when it was attempted (many times) it was deemed slower by the drivers of the times.

To quote WP "Meanwhile, advances in wing and tyre technologies negated any advantage to compensate for the extra weight and complication of their 4WD transmission systems compared to their rear-wheel drive contemporaries. Furthermore, virtually every driver who drove the cars hated the way they handled."

The added weight and complexity (lower transmission efficiency) means that the 320 hp EVO will be heavier than a 320 hp BRZ.
If you want to make the arguement:
2800 lb, 320hp 4WD EVO-X (they actually weigh 3500 lbs)
Versus
2800 lb, 320hp RWD BRZ

Then yes the EVO will win, but if you just take a stock evo-x against BRZ boosted to 320 hp, the BRZ should win the drag race.