It’s an interesting idea, but it needs work. It appears to be based on a French initiative (some things appear in French) and it’s a little hard to figure out its structure.
The default is the leaden NAB translation, although if you scroll all the way to the bottom, you can select the RSV, and then all the texts that appear will be from that version.
You're right, the NASB is leaden and not my first choice for general Bible reading. BUT, I use it exclusivly for word studies and close textual exposition because it always comes out closest to the original text. Have you checked out the English Standard Version? (ESV) It has become my favorite for general reading. Very close word for word but it reads much better and is more poetic than NASB. Some call it the updated RSV but I never read the RSV so can't comment on that. Most people who like the RSV like it.