Hemingway was a traditional, fiction, novelist and focused on his characters. Thompson defied (edit: was defined, oops) 100s of years of traditional writing (both novel and newspaper) by inventing so called 'gonzo' journalism. The man openly included his own personal life directly into all of this work, including this letter. He also, never worked in canada.
While I hold both men in high regard, the only parallels between these two men are the facts they both were journalists and authors (and drunks), since that's true for almost every published journalist, it's a thin comparison at best.
Also, if you consult HST's wikipedia entry, you'll notice Hemingway come up several times (and in fairly significant ways).
No disagreement on the similarity between those two, however.
When Hemingway started out, he worked for the Toronto Star (another Canadian newspaper). He wrote his first novel during this time: The Sun Also Rises, about expatriates living in Paris.
Hunter decided to apply to a Canadian newspaper after admittingly not being familiar with it. Then not long after he wrote his first novel - The Rum Diary - which was heavily inspired by Hemingway's first, about expatriates living in Puerto Rico.