On this, I will tell you - it's not about the story, it's about the characters and their interaction and banter. But even just the story alone - consider this. He's on an airplane to get the treasure. His airplane gets shot down by the same mercenaries that are later trying to kill him. At that point it's not about the treasure anymore, it's about saving your hide and getting off that island, and the only way to do so is stealing the boat from the very people who are actively trying to kill you, because they don't want to you around that treasure. Not sure how far you are, so without spoiling things, the treasure will only come into picture at a later point when it finally becomes clear what that treasure really is. Basically, throughout all the game, there's not a single point where you have any option but to either defend yourself, and try to escape, or die (or do something for a grander purpose later on). I wish the later two games kept that level of internal consistency of the morality of your actions, but they haven't done that entirely (although, they do in fact paint Drake as a darker, more rogue character than the first game does). Still though, in all three games, it's only the bad guys who die from your hand, and at several points you get to help the good guys and the innocents.
Overall, what I like the most about UC1 is that it has the level of intimacy both with the location and the characters that's rarely seen before or since. You travel the whole game in a continuous journey, mostly on foot, becoming intimate with the mysterious location. I really like when games do this (i.e. MGS1 and 3) and they have progressively abandoned that concept in UC2 (where you still spend most of the game in a continuous journey, but not just on foot) and UC3 (which takes place all over the world).