Honestly, I think both games are way overrated, but if I had to choose, it would be Half-Life 2. The thing is, HL2's story never felt at odds with its gameplay, as opposed to BioShock Infinite, whose story felt way too pretentious for its overly-generic first-person shooter gameplay. HL2's story felt like it was movie you and your friends watch over the weekend just for a couple hours of fun, and the gameplay backed that up. Infinite's story felt like it was trying to be that incredibly dramatic, thoughtful story that sticks with you for days after you finish it, but the gameplay was as far away from that style as you can get.
On top of that, HL2 actually did better with what it tried to do. Yes, it had a not-so-serious story, but it was a fun story to follow if you didn't try to take it too seriously. Infinite's story was meant to be complex and allegorical, but all it really did was come across as incredibly pretentious, and not in the appealing way that Braid was. That pretentiousness is only made worse when you consider the RPG genre has been doing everything Infinite tried to do for years, and the RPGs are generally better at it. Not to mention, other games like The Prince of Persia: Sands of Time Trilogy and Braid already told stories very, very similar to Infinite's, but they did it much better than what Infinite did (as in, Infinite isn't even the same league with them). Sure, HL2 isn't the greatest story ever, but it is a great example of how to just have fun with the story.
Finally, HL2 was better paced and more focused. Yes, places like Ravenholm were little more than filler material, but again, the story wasn't that serious to begin with, and who can go through Ravenholm without realizing that Valve wasn't taking themselves too seriously? Not to mention, the transitions from when you were interacting with people and going through challenges alone was smoother. You actually went over area that made sense when you transitioned from "populated area" to "not-populated area". Infinite's transitions between these areas was jarring, and it took a while to go from "wonderful populated mode" to "sort of boring combat mode". This jarring nature was only felt more when you consider the obvious transitions in themes (going from a commentary on American nationalism to timeline jumping?).
In the end, HL2 just understood what it was and what its genre was about much more than Infinite did. If we were to compare HL2 to either of the first two BioShock games, then I can see some competition here in terms of storytelling, but so far, I think Infinite is easily the worst example of storytelling the franchise has to offer. Oh yeah, and it doesn't help Infinite that its ending was just a boring, overly pretentious 10-20 min. of them explaining everything they failed to work into the rest of the game. Sorry, but any story that has to take time at the end to explain itself isn't good. I don't care if they add a few revelations that change your perspective on things, or if the characters finally realize what everything else in the story was trying to teach them (i.e. the end of character development), but that isn't what Infinite is. Infinite's ending is the game telling you, the player (not Booker), what its story is about simply because it failed to slowly and thoughtfully explain itself throughout the rest of the game.