OK, so the starting area is a bit silly, let's fast-forward to Primm. You invade a hotel that's held by convicts who have broken off from the main group of Powder Gangers. OK, most of them aren't that bad, OMG THE LEADER HAS A FRIKKIN' INCINERATOR!!! As a melee-centric character, I can say this encounter is pretty damn hard (almost impossible) without switchin' over to guns, and I really don't like to do that, or eatin' the med-x and stimpacks like a mo' fo'. Other than that it's pretty easy, get a nice number of guns, armor is pretty lacking, but what are you going to do?
I made a character in Fallout 3 that was almost impervious to harm even in the very beginning of the game without armor, and went around punching people to death while shrugging off point-blank bullets and the like. After going through the entire Vault punching everyone hostile to death while ignoring their bullets (and carrying
all of the armor, helmets, and guns out with me), I proceeded to walk up to super mutants and
punch them in the face. Guess what? It's
Super Effective. Works better than shooting them, and their attacks just glanced off my characters' innate Made of Ironness. This was all due to min-maxing my stats and using Perception as a dump stat (it was at 1 or something). I had int at 10, and str and end at 9 or 10 each, making the character both super-strong and super-tough.
My experience in New Vegas was that this doesn't work as well. I'd surmise that it was because the weapons and creatures were designed for the Damage Threshold system, and that endurance doesn't give you any DT. Running around with high HP due to high endurance, and expecting to be able to face tougher enemies than normal or punch everyone to death, presumably doesn't work like it did in Fallout 3 because the weapons are effectively far more powerful against anyone wearing inadequate or no armor, and useless against anyone wearing armor that is too strong for the weapon to get through. Your max HP is still important for determining how long you can last in a fight, but making it 3 times higher than normal generally won't let you win an unwinnable fight anymore (or leave the starting city and go punch Deathclaws to death for the lulz).
Note: I haven't played it with the new patch yet. Steam installed it the other day, but I actually started playing Morrowind again. I just stabbed a cliff racer to death with a spear while levitating, chasing it through the air as it tried to flee. Mwah-ha-ha.