To answer your main question, no you do not. While Fallout NV exists in the same world as Fallout 3, they don't have much of a connection story-wise and the absolute most you will miss out on are a few out of the way references.
As for if you will like it, it depends. Fallout NV is much more non-linear then FO3 with a branching main quest with multiple endings and MANY more sidequests (I think the number was about 70 to FO3's 30). The gameplay is mostly the same, but the quality of the writing is much better. However, the game is REALLY buggy, and you probably want to play it with the wiki open and the dev console on. That being said, Fallout NV is my favorite RPG in recent memory, so I suggest you go for it.
Oh, and hardcore mode really isn't all that difficult, it just means you can't do some of the cheesier builds like spamming stimpacks in the middle of a battle and you have to lug a few food items in your inventory.
As for if you will like it, it depends. Fallout NV is much more non-linear then FO3 with a branching main quest with multiple endings and MANY more sidequests (I think the number was about 70 to FO3's 30). The gameplay is mostly the same, but the quality of the writing is much better. However, the game is REALLY buggy, and you probably want to play it with the wiki open and the dev console on. That being said, Fallout NV is my favorite RPG in recent memory, so I suggest you go for it.
Oh, and hardcore mode really isn't all that difficult, it just means you can't do some of the cheesier builds like spamming stimpacks in the middle of a battle and you have to lug a few food items in your inventory.