Going by Spidery-biology, I'd posit Jessica being the stronger one physically. Possibly have them matched as far as actual flexibility and general coordination/dexterity and agility goes, but Peter having the edge on a more refined Spider-Sense makes sense.
While I kind of like the general idea on a single person getting Spider powers off of a genetically engineered spider's bite, having two of them develop similar powers, while good should probably have a way to make it more interesting.
Perhaps the actual 'spider powers' in this case are a sort of heightened/modified bioelectric field. Something that lets them duplicate spider abilities. It's pretty much cannon that Spidey's wall-crawling involves molecular charge suppression. Kind of like a weird high-level static cling. If all the powers had a bioelectrical basis... such as the enhanced agility and coordination being brought about by a more efficient nervous system. Maybe all the additional electricity is able to supercharge their muscles to allow them to work well past the expected mechanical limits. With this as a sort of basis for 'spider powers' we can come up with a couple of additional possibilities for some variety, while still having the same common base.
Peter could still have the standard classic Spider-man powerset. Enhanced agility, strength and durability, wall crawling. The Spider Sense could be a bioelectric aura around himself that lets him know of any motion within its range. Jessica in contrast while getting the agility, strength and durability, stick to walls, but to slightly match up with the original Spiderwoman's powers even if just a bit, she can release her bioelectricity in non-lethal shocks, her version of a spider sting. I'd even go so far as to have her shocks make whoever she's just hit become more suggestible when they initially wake up. Perhaps she'd also have an electromagnetic repulsive ability that potentially could make her good at throwing things, but could also be used to let her boost her jumps in mid-air (sort of like a double-jump), but could potentially be mistaken for gliding.
With the contrasting power set, I'm also imagining Peter being the more cerebral one. So I'm imagining his more refined Spider Sense could also be tuned to trace electrical signals. Peter would make the web-shooters to make up for his lack of a ranged option, while Jessica might carry something like darts that she can charge with her sting and then repel away from her into her targets. She doesn't need to web-shooters quite like Peter does since she has her sort-of gliding ability, but I can't imagine Peter not giving her a set either.
Also, the outfit is most likely designed by her and specifically meant for her, which is why when they do finally go out, the cut looks all wrong on him and people think he might just be a particularly flat-chested women.
"I hope you're happy. They think we're calling us the Scarlet Spider girls."
"Well, what do you want me to do? Sew on a bigger cup on your outfit?"
"For starters!"
