Nope, the Like button has always used the URL, so Facebook doesn't have an 'old' vs a 'new' version to cause this confusion. You should be able to use {JFBCLike} without any problems. However! we'd recommend that you specify a URL to make sure that it's always the 'right' URL that someone Like's. For example, if you have SEF URLs enabled, and the night dive page is /night-dive, that page may also be reachable at /index.php?option=com_content&view=article&id=12. If someone stumbles on that non-SEF link and Like's it, that's a separate page from the SEF version, in Facebook's eyes, so you'll be splitting your Likes.
However, however! If you're using the Open Graph tags on the page to specify the URL of the page (the canonical URL), then even if on the non-SEF version, Facebook will know that the Like is intended for the SEF URL specified in the Open Graph Tag. This is why the move to the 'new' comment box is a good thing, because the comments are attached to a URL, which can be manipulated with some of the Open Graph stuff.
Finally, our JFBCContent plugin to automatically insert comments/likes into articles will always insert a URL for the page the widget is being added for, so the comment issue isn't a problem for that.. only when you use the {JFBCComment} tag or Module with no URL specified.
Whew.. confused yet?
P.S. I want to go on a night dive! Haven't been on one in 10 years, but loved it.
P.S.S. Your engageyourdivers.com site, using chrome, is showing the TapThemes template. Not sure if that's intentional, since that's for mobile stuff mainly, but thought I'd call it out.