Their lives weren't identical. Jango's parents died about the time he was 10, but Jango was adopted by Jaster Mareel, and therefore grew to be an adult with the help of a parent, and the Mandalorians. Boba was thrust out into the galaxy on his own. Jango didn't start being a bounty hunter till after he broke free from slavery which the Jedi sold him into after the Battle of Galadrian. He was well into adult-hood by that point. Boba grew up around Jango, started learning the ways of being a bounty hunter since before he can remember. And their personalities are a little different as well, for example Jango goes around helmetless sometimes, especially at home. Boba never goes without it, and as far as I know Slave I IS his home. So one of the main differences is that Jango, drifting from family to family with the period of slavery exempt, (after that it was Roz, an employer, and after that he had Boba) he was probably a little softer because of that. Boba, having no one after age 10 had to learn to be a little rougher, and a lot earlier on.
And I agree that people already having the idea of "Fett" being someone you don't want to mess with helped him out a lot.