Maybe I didn't fully understand the question, but it's pretty obvious that you get more likes and shares staying on FB, since FB is by far the most prolific and effective social network in the world, whose main goal and expertise is to generate likes and shares.
But that doesn't mean you can't send users outside. Most of the time you have to send them elsewhere, because most products don't operate within FB.
In any case, if you do redirect users to your site off-FB, you can redirect them back using embedded "like" and "share" buttons on your site.
Last year I did a social project on my website and mostly promotes it organically via FB. The website had embedded FB buttons featured prominently at just the right spot (which users reach after using the product and, hopefully, being impressed by it). About one out of 6 visitors (or almost half the users) had pressed the "like" button, thus effectively sharing my website on FB. The website became very viral, largely thanks to this arrangement.
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