IMHO, hardcoe mode adds a simulated layer of realism that further differentiates the FONV experience from its FO3 sibling.
The game just feels different when you don't have the luxury of carrying every piece of ammo you find in the wasteland and because stimpacks heal over time you need to think twice before engaging tough enemies such as Deathclaws or a swarm of Cazadores.
You also have to worry about your companions since they aren't flagged as "essential".
I also like the fact that there is a use for food/water and rest in the game. Without hardcoe, aside from the well rested bonus, beds are pretty much just for show and food and drink aside from what paltry status and healing bonuses they may have, are more or less just slightly more expensive junk.
Also doctor services are much more valuable since you want to save doc bags radaways for the field, in FO3 they were practically useless.
As for weather or not it makes the game harder, with respect to the weighted ammo, healing item delays and killable companions, yes it does.
Though I do have to say that the term "hardcoe mode" may be a bit of a misnomer, since it's more of a "realistic simulation" mode. If you truly want something hardcoe, try a "dead is dead" playthrough...