You asked about UC characters and story, I wanted to answer a bit more but didn't have the opportunity.
UC1 and UC2 spoilers ahoy
Nathan Drake is a watered down mix of Indiana Jones and Han Solo. When he has a sense of right and wrong about something, he falls into it easily and intensely. But he's also a shallow jerk to everyone, and we forgive him these trespasses because he's attractive and talented. He admittedly doesn't think very far ahead, and his plan to double cross Flynn backfires, yet his shallow nature permits him to begin thinking he is the victim in all of this, and continue to hold onto that notion. While this plays into the "among thieves" line, it still shows Drake as a narrow-visioned guy who rarely thinks beyond what is immediate to him.
In UC1, Drake is just an action hero with some funny little comments, a drive to follow his ancestor's path, and hey let's save the world too. It's odd that he is so intent on saving the world when he's really more of a scavenger, but if you head off into the sunset with the girl, the gold and having saved the world? there's really no characterization you need to worry about at all. So coming out of that game, Drake is fairly meaningless. He's not even a mascot.
UC2 Drake is a bit more puzzling. He ditches Elena and has moved onto Chloe. Elena and Chloe even joke about it being a "last year's model" situation. Drake spends much of the game risking everything to bail out Chloe, who has double crossed him. Elena gets randomly pulled into it, and at the end... Drake loves Elena. Drake's own actions suggest entirely the opposite, and without any real means of exploring his intentions or struggles (we don't even manage generic afraid-to-get-close tropes), he's actually interested in Elena. It seems to be meant for the gameplayer and not the character. in this sense Drake is a perfectly realized juvenile male romance novel character, but as an actual character, poorly realized. If we just want a guy who just jumps and shoots and looks good enough to get whatever he wants, that's Drake. We're just lucky that what he wants is treasure, and by wanting that treasure, he stumbles into very specific opportunities to save the world. And we're lucky that he wants to save the world, though it doesn't really fit any moral set we've uncovered through the first two games.
The stories are fun. They're action movies. The villains are terrible. The village in UC2 actually adds a bit of texture to the series but they just blow it up with a tank. When it gets to the end of the village, you blow the tank up.
There's certainly no reason to be invested in the characters, though they make for a fun ride. And Elena isn't terrible.
I will say that UC2 does a great job of changing the action up. Plenty of action sequences are designed around you having various vantage points, or using stealth, etc. It's not just generic/poor cover shooting like UC1, though that does show up a little bit because the cover shooting mechanics are still probably third rate. But, let's consider the part where Elena and Drake are up in the mountains and they need to open a gate, so Drake climbs up and around and is on top of a gutted building that has enemies all the way down. Right here we can shoot our way through, stealth our way through, or stealth our way to a point where we have a combat advantage. That's terrific. It's probably a better realized sense of what stealth should be than anything in MGS aside from the Tanker.
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Donny: Are they gonna hurt us, Walter?
Walter: No, Donny. These men are cowards.