A few years back, FFG released a book of short stories based on the investigators that show up in all the Arkham Horror Files games, and as part of the promotion for that book they published
this article that among other things describe some of the differences between Arkham Horror and classic Cthulhu Mythos.
Edit: as an example of the somewhat more pulpy bent, once we were playing Arkham Horror (2nd ed) with Hastur as the Great Old One. One of Hastur's game effects is that it's
much harder to seal gates (which is one of the ways in which you win the game). We had some seemingly bad luck in the early game with lots of gates opening, and realized some things:
- We were probably not going to win the normal way, by sealing enough gates before getting enough Doom to summon Hastur.
- Hastur didn't have any particular resistances.
- Hastur's combat modifier (how difficult fighting him is) depends on the Terror Level, which is something that normally escalates through the game when too many monsters show up.
So we basically ignored gates, and instead focused on getting weapons and killing monsters. It didn't take too long for Hastur to show up, but he only had like a -2 to our combat checks, so we handily kicked his butt back to Carcosa. Fastest game of Arkham we ever played, only took like 45 minutes.
Anyhow, the point is that in Arkham Horror, a hunting rifle can be a completely reasonable way to prevent a Great Old One from destroying the world.