-story : either
-gameplay: new vegas
-feeling: ? new vegas
-scary parts: fallout 3
-mechanics: either
I personally like New Vegas a bit more, it is a bit more immersive, but Fallout 3 was really great because it was definitely set apart from Fallout 1 and 2 because of the setting being on the East Coast, but New Vegas is really cool because the Mojave wasn't as affected by nuclear devastation like DC was.
When it comes to DLC though, or the ultimate editions, Fallout 3 is more stable as New Vegas definitely has had a lot of problems with their DLC. The vanilla game though, I'll take FONV over FO3.
It's really a give and take on both, and imo the deciding factors would be if you plan to play the DLCs or not, and more importantly what is a better setting for you. If you want to see more active landscape in terms of nature, New Vegas is for you. Want to explore more ruins and destroyed city? Fallout 3 is the answer.
You really can't go wrong with either one. Oh, when it comes to gameplay and mechanics, I like New Vegas simply for being able to aim down the sights of a gun. Other than that, the differences are really subtle. New Vegas is a bit trickier with it's perks than FO3 because many of the perks are double edged swords type of deals, where Fallout 3 they are all positive effects.
When it comes to the main story, both games have huge differences. Fallout 3 you follow the same main quest, but you have an actual traditional alignment system of Good, Neutral, Evil. Depending on what you do will depend on the final outcome. New Vegas gets rid of this and has more of a reputation system with not only the 3 big factions of the main quest, but every town and group as well and way more in depth in that regards, but it has no alignment system because of it is recognized in New Vegas that Good, Neutral, and Evil are all matters of perspective depending on whose eyes are looking at upon you and your deeds.
If you want to get more into survival mode in post-apocalyptic city, Fallout 3 is more suited. However in New Vegas there is an actual "hardcoe" mode where your thirst, hunger, and rest are measured on a scale similar to radiation. Also nothing heals you instantly except for sleep and doctors bags, stimpacks are gradual healing over time, and also to take advantage of them you need to invest into medicine. Though you don't really need to because if you invest in survival, food that you find or make can have better results.
Fallout 3 is really good, it has a great feel for the game but when it comes to survival mode, New Vegas is better. If Fallout 3 had that hardcoe mode it would be hands down better than New Vegas in that regard because of the location of the game itself.
There is so much to elaborate on the similarities and differences with the two games, both are done well and offer their own unique experience. I could go on and on about the differences, but that would be just an incredibly long post. Though if you have a specific question, would be much easier to elaborate on something.