Based on my experience in Apple design reviews and industry best practices, a rule of thumb for apps is to always use the native iOS controls whenever possible. The laundry list of why is long, but the general idea is this is the most seamless way to take advantage of every iOS update for sharing and it's been vigorously tested and proven before release from Apple. (With proper testing on your app's implementation of course.)

The documentation is pretty easy to find on https://developer.apple.com but you have to become a member. If you are unable to sign up, an easy way to see this functionality visually cataloged is with Teehan + Lax's latest UI docs. http://www.teehanlax.com/tools

Once you see the native share control visually, go to your favorite apps and industry leaders to compare and contrast. You may even want to create a spreadsheet with screenshots of each and detail the interactions before you make a decision. (Or it may be totally obvious.) It all depends on your app's feature set and needs.

As for web, it's wide open and more information would be needed before I could recommend an approach. I'm available for a call and I'd be happy to dive in with you.