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There's no such thing as the "big stack aggressor advantage".
Ed Miller wrote an article on this called
The Biggest No-Limit Hold 'Em Myth.
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Notice that he says "inherent mathematical advantage." There is almost certainly an advantage at least up through midstakes. Most of it is psychological. Some of the fish will take shots at you while others will shy away. I got labeled a "poker pro" last night at the tables when some guy saw me sitting on 4.5 BIs on one table and 5 on another. This guy was playing every pot I was in on both tables because he "wanted to bust a pro" as he said in chat. This would not have happened had I been sitting on 2 BIs or less.
Furthermore, you can increase the variance of the game if you so chose by playing hands a lot faster and bluffing more (you can do this if you have more BIs overall for a level than others too). If you are evenly matched and you increase the variance and have more money then you will get it all faster.
There definitely are advantages to playing a big stack, but not the "inherent" ones that are built into the game which is what Ed is referring to.