A few thoughts:
One thing that definitely improved is the writing. Unlike Fallout 3 where everything is actually fairly clear-cut trough the veil of grittiness, you actually get the idea that most of the factions have their ideology and history. Ceaser is a warlord with a fancy theme, the NRC is like a modern government (it means well if you ignore its greed, corruption and occasional incompetence) and Mr.House wants Vegas to be his. The character work is improved too, you genuinely get the feel that these people live in the world you are in rather than fanfic-inserts. All of the companions, even the dog (although that's hinted), has a bit of history they can tell and have their own view of the world (you can ask about their opinion about various factions).
There are more speech checks too, meaning that you can solve a problem diplomatically with something else than just Speech. Repair, Barter, Medicine, Survival and Science (and even gun skills) can help you solve quests through dialog.
More quests can also be solved multiple ways and less rarely your usual "kill 20 rats in the cellar" type stuff. For one thing, the quests are a bit more logical, sometimes requires a bit of investigation and written well (unlike in Oblivion where you were everyone's favorite *****).
As for Hardcore mode... Yahtzee is right, it doesn't add that much. It's just means that you need extra health items and a new skill (Survival, which to be fair, also allows you to make certain drugs, make more use out of skins/meat and is actually a sort of alternative to Medicine). It tries to add a new dimension to the game, but the truth is, that once you are past the breaking point of difficulty, you trip over most of the health items you need. Not that it's bad mind you, just needs more depth.
Crafting is more ingrained though, as you can craft ammo and health items. This also sort of combines two skills, as you can craft Gun items with Repair (you can re-make bullets too) and Energy weapon ammo (which ammunition you can recycle) with Science (making it useful for something more than just occasionally cracking a terminal). Also, with Survival, you can make poisons that you can use with melee weapons. However, I dislike that there are less crafted weapons.
The bugs can be annoying, ESPECIALLY on console however. I'm not cheating or modding (much) but there is actually a DLL file out there that will massively help improve performance, as well as certain issues. Still, I have already learned some console commands to play trough the game (especially companion teleporting because the fucks constantly get gliched or lost).
However, these will likely be fixed over time and I would rather take some bugs over boring quests with uninspiring stories.
Overall, I think it is an improvement over Fallout 3.
