I have played through this game a few times, I have played Fallout 1, 2 and 3 previously and here are some of my very biased thoughts and feelings on the game.
These are my opinions and are in no way reflective of objective reality or truth.
I want to start off with saying that the fact that this game was finished in such short time is amazing.
For this game to be so stable or not as unstable as it could be after a mere 12 month development time is quite a feat.
It IS a buggy mess as is the Obsidian staple but it could be way worse given that it was programmed in about 10 months.

This is the game in the Fallout series I like the least.
Most of it stems from the blatant views of Chris Avellone.
Grey and grey morality? Check.
No romances, no happy love/romance. Check.
Mute and bald girl. Check.
Deconstruction and author avatar in this case Ulysses. Check.
Sad, bad or bittersweet and no good outcome endings for good guys. Check.

Sometimes I imagine Chris sitting in a dark corner frothing at his mouth screaming:
No love! No happiness! No happy romances!
Grey! Grey! Grey and morality! No black and white! Hose it down with grey!
The good shall suffer! They must suffer! Bad guys are the best guys! They get all happy endings and are the best choice!
He loves his suffering and drama he does.

There is a lot of Van Buren in New Vegas, IMO much to it's detriment.
Most of the things I dislike are the Van Buren and Chris Avellone inspired parts.

One major thing about the factions that irks me in particular is the Brotherhood of Steel and the Enclave remnants.
This is the only game where I don't want to join the Brotherhood, their character development and progress in Fallout 1 and 2 almost completely derailed.
They are all almost all idiots now and this Codex makes no sense and seemingly came out of nowehere.

The Enclave remnants are one of the most blatant examples of whitewashing I have seen in recent years.
Oh, these guys are so sympathetic, you should feel sorry for them for being bullied by the nasty NCR.
Some people like them a lot and disregards the twice attempted genocide plan, first time in Fallout 2 and the second in Fallout 3.
Where were these guys when Vault 13 got brutally gunned down?
When Frank Horrigan slaughtered the people in the desert where were these sympathetic people?
Or when the Enclave did deals with the Salvatore?

The NCR never were the good guys, they were less villainous than most factions, but newer a Utopia as shown in Fallout 2.
It is IMO a good balance, the NCR had itr's problems and the progress of corruption is more believable than the 180 turn of the BoS and the Enclave Remnants.

Caesars Legion however is my most loathed faction.
As a faction and as villains they make no sense, even admitted by Caesar himself that they are more like the raiding barbarian Gauls than the disciplined Legions of Rome.
Their leader is a hypocrite and his whole motivation and idealogy only would make any kind of sense if one has a brain tumor.
Medicine and science weakens people but it is OK for their glorious leader to use scientific medicine and medicinal tech to cure his brain tumor.
What...?
It needs to be added that I dislike unecessary suffering IRL as well and the Legion are all about unecessary suffering,

As for the gameplay itself, not really impressed.
Most quests kinda meh. Uninteresting characters, skill checks, quests not impressed.
One thing I do like is the abundance of medicine skill checks, performing diagnostics and surgery is something I really like in games, especially Fallout 2.
Combat, meh.
I have never been into combat, I prefer diplomat characters overall but New Vegas combat is at least to me the least well done of the series.
What's up with the tons of different ammo types?
I much prefer the combat in Fallout 1 and 3.
Just my opinion.
I also question the choice of making some unique weapons less attractive choices.
Overall I much prefer a modded plan variant over some of the unique guns.
Ratslayer being one obvious exception.
Fallout 3 did it better, the unique versions were not always the best, but often better and more usefl/efficient than the plain vanilla variant.

The Pip-boy interface works less efficiently than in Fallout 3, at least for me.
The Faction system feels shallow and tacked on.
It just doesn't feel right or work well compared to Fallout 2 which did it better in most regards.
At least it follows the trend Obsidian has of getting nearly everything handed to them on a platter, having nearly everything already done for them and turning out an a worse looking, more buggy sequel.
Neverwinter Nights 2, Kotor 2 and now Nev Vegas.
I absolutely adore Kotor 2 for the themes, setting and a lot of the quests and grey and grey morality and the characters but I cannot deny that visually it looks worse than Kotor 1 and is horribly buggy and broken in a lot of ways.
Though I don't rant and rave or hate the endgame, sadly it was rushed but it is a testament of Obsidians programmers skill that it turned out as well as it did.

The big issue I have is with how perks work.
One perk every 2 levels doesn't work as well as in Fallout 3 where every level got a perk.
In Fallout 3 I was never near getting all the perks I wanted, most of the perks worked well and were overall well balanced and even integrated into conversations and quests.
In Fallout 1 and 2 one perk every 3rd or 4th level was even worse IMO.

Music is overall good, I especially like the themes from Fallout 1 and 2, very nostalgic.
I prefer Three Dog to Mr New Vegas who is so obviously an AI.
Three Dog has more personality because he is a person. Heh.
Pretty much all the songs are forgettable at least in my case.
I suspect most people feel different and are not of my opnion in this and all of the above stated points.

The DLC I enjoy the most is Old World Blues and Honest Hearts and I loathe Dead Money.
I've always had a soft spot for mad science and the tribal bits in Honest Hearts is something I have missed since Fallout 2, Point Lookout doesn't feel like real tribals to me, more like lobotomised mooks.

Continuity, loved seeing Marcus again. If you could vote for a Supermutant I would vote for him to become President.
The Vaults from the Fallout Bible such as Vault 34 and 21 were highly enjoyable for me.
All the references and continuity nods to the previous games is an absolute delight, the Veritibird crash in Klamath to Mr Bishop. Hehe.
Though my Chosen One wouldn't get that particular ending, but whatever.

Overall view: New Vegas is in no way atrocious, horrible or awful, it is only a few design, gameplay, plot and character choices that I personally find to be railroaded and poorly thought out.
IMO it is the weakest of the series, my personal favourite being Fallout 1.
But it is a good game and my whining is in no way an indication of poor quality. but a personal biased viewpoint and subjective feelings.