I had a much more positive reaction to the quality of Batman Arkham Asylum at its launch in 2008 than I did for Spider-Man in 2018 but I think I like Spider-Man more, and I think that's largely because I enjoy Spider-Man as a character more. They both have tremendous hits at representing qualities of the characters that I enjoy, but also both have weird new quirks. In Spidey's game, working with a direct communication channel to police was weird; in Batman, the last boss was super weird story-wise.
To elaborate a bit, in 2008 I didn't expect a great, polished take on Batman from a licensed game. In 2018 since Spider-Man was being developed by Insomniac, I had high expectations before, so the gap to be covered between expectations and reality was a lot less than Batman had in 2008. I had never heard of Rocksteady before in 2008, and admittedly I wasn't a fan of the gritty "Unreal Engine 3" esque visuals of Batman prior to playing it, but felt that it worked well once I actually did play it.
I voted Batman based on the question in the OP, though... Once again I did not read the poll question/the poll question did not line up with OP.