Brace yourself. Long read.
There's nothing really wrong with Fallout 3's writing and presentation, nor is there anything wrong with New Vegas'.
Both games present their writing with different philosophies and manners. Fallout 3 has a generally clear right and wrong with black and white morality. New Vegas doesn't.
Fallout 3 puts you on a road to destiny and a clash against evil, despite your karma stance. Good and evil are generally clearly defined with very few choices of in between, and even then, those are generally the 'fuck this shit lmao i'm out' kind of true neutral.
New Vegas lets you start as a literally fucking who, build up your legend, and have a bigger effect on the world, but one you earn for yourself, instead of just having it be handed to you as you walk along.
Neither are bad or good games objectively speaking, however Fallout 3's story of the super good saints vs the evil dicks is pretty cliche and has been done shittons of times before, and isn't what people have come to expect from the Fallout franchise, considering 1 and 2's wide moral scale.
That said, New Vegas gets a lot of unfair dicksucking from people who have probably never touched 1 or 2, because it doesn't follow Bethesda's conventional story style. I've been going through Fallout 3 and New Vegas lately, and the differences between the stories are incredibly apparent. It's an issue of style, however. Not of quality. For every "trust me, i have high speech" thing you hear about in Fallout 3, you can find similar shit in New Vegas.
Both games have their flaws, and both games have their merits. I think it's unfair to say one is objectively better or inferior to the other based on this. They're different styles of games by different developers, for different fanbases.
Take the hate you see for 3 over NV with a grain of salt, because it's NV's demographic being mad that Fallout as a franchise isn't done in the same style anymore.