The most important similarity between Jeremiah Johnson and Chris McCandless is their shared desire to live a simple life, alone in the wilderness, with only nature around them. Neither got quite the result they wanted: Johnson was constantly beset by troubles, and lost both his adopted family and his innocence; Chris never prepared properly to survive in the harsh Alaskan wild, and died of starvation. Both took little notice of societal conventions (such as knowing or caring about the time of year) and both faced tremendous hardships in the pursuit of their dreams.
Their differences are more apparent: Johnson sought peaceful life alone in the woods after fighting in the Mexican War, and only wanted to escape what he felt was the Western focus on war and materialism, only to find that the Natives and other inhabitants of the wilderness were equally violent; Chris deliberately lived a life of poverty, abandoning his material possessions in a quest to discover his own meaning and the greater meaning of life. Another difference is in their actions: while Johnson tried to live peacefully, he fought for his own life and took revenge when he felt it was justified (and out of emotional grief); Chris was a pacifist who never clashed with others and he only killed animals to eat, never for sport.
One comparison comes within the text, when Chris's father Walt recalls how he attended college for the first time:
The roommate was a preppy kid from Connecticut, dressed like" Joe College, and Chris walks in with a scraggly beard and worn-out clothes, looking like Jeremiah Johnson, packing a machete and a deer-hunting rifle.
(Krakauer, Into the Wild, Amazon.com)
Walt goes on to say that Chris made Dean's List, while the "preppy kid" dropped out. This comparison is entirely superficial, but it goes to show more of Chris's personality; he didn't care what people thought, and he was a hard worker in any venture he undertook.