In areas where a community is willing to invest in beach restoration or nourishment, it is typically because there is a sand shortage. One of the biggest problems with using structures instead of sand is that structures do not "create" more sand. Offshore structures work to slow or completely stop the movement of sand along the beach. This is the same whether a structure is perpindicular to the beach like a groin, or parallel to a beach like a breakwater.
Assuming the offshore structure is working well, let's take three houses as an example, A, B, C. In this case, sand is moving down the beach from A to B to C. House B places an offshore breakwater. Now, the same amount of sand moves from house A to house B, but due to the effectiveness of the structure behind house B less sand is moving to house C. Typically, if you have an eroding shoreline before you install a structure like behind house C and that area begins receiving less sand after the structure is installed, that stretch of beach would be at an even greater sand deficit and thus more erosion. All this being said, structures are sometimes used in conjunction with beach restoration to assist in holding the sand in place. Once again, it's a case of site specific needs and one alternative definitely doesn't fit all locations.
As for the project you linked to, I believe it is being funded as an innovative technology and will have a rigorous experimental test plan to evaluate it's effectiveness. I hope it works also as it would be a very innovative approach. One cautionary note. In the late 80's or early 90's (I think), a submerged reef, called the PEP reef, was constructed along the east coast of Florida and in its lee there was more erosion due to the pumping action caused by the interaction of the waves and structures. Waves came over the reef, and then rushed around the edges like a rip current looking for a location to get back out since it couldn't go over the constructed reef.
One final note, the website mentioned naturally occurring reefs as an example. A big difference between our area and naturally occurring reefs is that reefs produce carbonate sands that move onto a beach. Thus, new sand being created and arriving fairly constantly. Our sand is silicate sand and we have a limited sand supply that was delivered thousands of years ago from the Appalachian Mountains.