In regards to "Living the American Dream," who succeeded? Gatsby from The Great Gatsby, or Chris from Into the Wild?
This question depends mostly on how "The American Dream" is defined. For some, it is the acquisition of money, for others, a family and friends. Some people think that power is the American Dream, while others consider charity. In both of the mentioned books, there is a definite disconnect between the characters and whatever their personal American Dream might have been.
For Jay Gatsby, he has on the surface achieved one version of the Dream: he is wealthy, popular, and influential. However, he never really cared about the money and popularity; he earned all of his money and status in the pursuit of one goal: to find and woo Daisy. This was his Dream: he wanted to prove his worth to her and prove that he loved her more than anything else. While he professed his love, he lost her at the end.
For Chris McCandless, he also achieved one sort of Dream: he traveled, touched many lives, and found enlightenment through isolation. His dream was shared by other travelers, but not fully understood by most of the people he met. It is most clearly laid out by comparison to another traveler with similar ideals:
"[...Everett] and McCandless, at least they tried to follow their dream. That's what was great about them.They tried. Not many do."
(Krakauer, Into the Wild, Amazon.com)
Chris wanted to discover himself and his purpose through communion with nature, and to an extent, he succeeded. However, he was unable to return to society to pass his message on to others, and so his victory, if he considered it so, was entirely personal.