I spent a chunk of yesterday reading various "Cass versus" match-ups on different message boards. One for some reason posited a cage fight between Cass and an oddly de-powered Spider-Man. The discussion that followed was full of RPG-derived jargon and terms like "nerfing," none of which I'll go into here. When I talk Cass-fights, I'm approaching them from a practical, reality-based standpoint (as much as possible when discussing superheroes and magical beings) and as a writer might.
Unfortunately for Cass, Spider-Man is quite a bit out of her power range. As I previously discussed, she may even have a problem reading his body language and predicting his moves if his movements happen to incorporate anything spider-like. This might even be something Spidey's less sensitive foes would never have noticed, but to Cass would be like an irritating buzz just inside the hearing frequencies on some slightly flawed master tape to an expert audiophile. That's just the start of her problems.
I believe Cass would be able to land quite a few blows despite Spider-Man's own spider-sense power and his beyond-human speed and agility, but the Wall-Crawler also possesses incredible resistance to pain and injury. Otherwise his web-swinging acrobatics would have snapped his all-to-human neck or he would have succumbed to any of the number of high-powered blows he's experienced through the years. With her predictive senses only somewhat helpful, Cass still finds herself tagging Spidey, but unable to deal him serious injury. Meanwhile, she proves vulnerable to his attacks-- and remember, his strength level is well above an ordinary human's. Spidey finds Cass very nimble in her own right and capable of dodging some of his punches and kicks, but he's pounding her a lot more than she's pounding him.
Cass might be able to learn some of Spidey's more human-like moves and attacks, but her body-- as peak conditioned as it is-- remains that of a base line human. Cass's fantastic martial arts prowess is ultimately no match for Spidey's freakish nature and greater experience. The resulting fight is brutal, goes on a little longer than Spider-Man might expect or like, but in the end, Cass succumbs.
And that's without Spidey having to use his web-shooters. What if he did employ them? Well, I don't think Cass has much a defense against those, and even if she did, Spidey could possibly whip up enough netting to gum Cass up but good. She could probably find something in her utility belt to free herself, but not before Spidey closes for the coup de grace.
On the other hand, a likely scenario would be the cliched meet-n-fight followed by a team-up where they take down Kingpin who's allied with Penguin for some nefarious scheme that stretches from Gotham City to New York City. If I wrote it, however, I'd just combine the two settings into just New York, with Gotham as its nickname. No cross-dimensional shenanigans for this cross-company cross-over if you please!