This was my first time playing through the Uncharted campaigns. As a package, it's a fantastic deal! Uncharted: Drake's Fortune (the first in the series) is the shortest campaign (7 - 8 hours on normal) and by far the least polished. However, for a game that's about 8 years old at this point (2007), it holds up well. Uncharted 2: Among Thieves was excellent, with more variety in locations, bigger set pieces, and a far more interesting story to tell. The combat and enemy variety also felt significantly improved. Uncharted 3: Drake's Deception was absolutely my favorite of the three campaigns, full stop. A great example of story telling, character development and gameplay all coming together seamlessly. It's also easily the best looking of the three campaigns, but that should come as no surprise.
Since this is my first time playing these games, I can't speak to improvements over their PS3 counterparts. The games have several difficulty modes, including two new modes for each campaign: An extra difficult mode called Brutal difficulty which is unlocked after beating the games on Crushing Difficulty (the highest available in the original games), and Explorer Mode which is super easy and meant for those just interested in the story. They've also added Speed Run Mode, which helps keep track of how quickly you're beating each section of the game and compare against your friends. Each game also has it's own set of collectables to hunt down, which allows for the unlocking of trophies and in-game modifiers like skins and access to weapons.
Having said all that, the game suffers from it's lack of any multiplayer. It's a confusing omission given that both Uncharted 2 and Uncharted 3 had highly rated, if maybe a bit underplayed, multiplayer modes. Perhaps they wished to avoid the issues that Halo: The Master Chief Collection encountered at it's launch, or maybe it was too complicated given the drastic differences in architecture between the PS3 and PS4. Regardless of why the decision was made, the game ends up being worse off for it. Sony/Naughty Dog try to offset this by offering access to the Uncharted 4: A Thief's End Multiplayer Beta coming December 2015, but you need to still own The Nathan Drake Collection in order to access it. I decided that access to a Beta wasn't worth holding off on trading the game in for less money down the road. If you don't normally sell or trade your games in after completing them, then that will be less of a factor.
Bottom Line: If you've never played the Uncharted campaigns before, I would absolutely recommend this collection. However, there's not much of a reason to keep it around once you've played through them unless you want to try harder difficulties, find missing collectables, or trophy hunt.