The first time they meet Spider-Man wins.
Extra details.
- Spider-Man is very super human. Batman is superhuman despite having no powers (through martial prowess he has defeated in a pure melee brawl characters like Bane, who are very super human as well, but Spider-Man should be many times stronger physically), and has the spider sense advantage
- Batman doesn't just carry his strongest arsenal around. Many times he has carried a Sinestro ring around just in case, but I'm assuming this is casual mainstream Batman on a night stroll and he's not.
- Batman has soloed the League before (with prep) and even negged Cyborg (without even knowing him) when they met for the first time.
- Spider-Man is smart, a genius, but he is not smarter than Batman. Batman can 100% outsmart him, it's his whole thing, and he's outsmarted in canon even greater minds.
- If Spider-Man is holding back, Batman can take advantage of that (callback to "He could use his superspeed to squish me into the cement, but I know how he thinks. [...] he's got one big weakness. Deep down, Clark's essentially a good person... and deep down, I'm not").
- Having said all that, most Batman can hope to achieve in this specific scenario is to escape Spider-Man. Nothing in his casual arsenal (assuming there's no Sinestro ring involved) can take Spider-Man down, while Spider-Man definitely has the means to capture him or put him down.