Lots of great comments. I have a couple of things to add.
US Sailing is analagous to US Fencing, US Gymnastics, US Archery, US Rowing. That is, they are the US governing body for Olympic sailing. They manage qualificiation paths and selection of the Olympic Sailing teams. That is, of course, when Sailing is included in the Olymics. Their primary mission is to identify Olympic atheletes. It is in their interests to promote all aspects of the sport as you never know where the next star will come from. They need an extensive paying membership to support this primary mission. I am not saying that this is a bad thing. This is why they are viewed as primarily a racing organisation.
ASA is primarly an organization focused on education of cruising sailors. Credentials are nearly universally accepted worldwide by charter ourfits. Of course credentials are not the only qualificiation to charter a $100k+ vessel.
Classes from each qualify as "Safe Boating" courses.
As far as insurance discounts go, I too have heard that these courses qualify a person to get some discounts. I have no fist hand knowledge as mine is a commercial policy. Some posters have said that they see no benefits to their insurance rates.
Some may find this report by the USCG interesting:
If you look at page 62, you will see "Number of Injured Victims by Primary Injury and Vessel Type". Note that out of 3000 total injuries, 2691 were caused by a power boat and 84 were caused by a Sailboat. This makes sailors in general a very safe group. Of course we knew that.
What I really wanted to know but could't pull from the report was the impact on boating education and casualty losses. I would predict that Sailors who have taken Safe Boating courses are, statisticaly, among the safest on the water.
Conclusion: Take a class. ASA or US Sailing