As with most things fit-related, it depends. If your body is longer on arms and legs and shorter on torso, a “women’s-specific” frame geometry might fit you better, because that’s the assumption those frames make about how women are shaped. It’s not a great assumption, since we now know that there’s more variation within genders than between, but the end result does fit people shaped that way–men or women–better than “unisex” frame geos.
The other advantage to “women’s” bikes is that they usually get stocked in stores in much smaller sizes than “men’s”/“unisex” bikes. If OP is 114lbs, that may be important.
OP, your current bike that fits you perfectly does have a “women’s-specific” geo, so you might fit well on more of the same. Specialized, Liv, and I think Canyon all do different geometries for women. You might fit great on a different geo too! Try everything, try all the things. Go to your local bike shop, ask to see the best aggressive road race bikes in every brand they have, test ride them all. With a 10k budget, anything you get is going to be very high quality, so it’s going to come down to what’s comfortable and what’s got which bells and whistles.