I am not sure that you can join RGSB through ARRL. I'm not finding it on the ARRL website. Perhaps it was a promotional effort, limited by time in some way.
I am a member of both. I usually renew each year at the RGSB boot at Dayton. I have not checked lately, but there may be minor savings if you buy RSGB books from ARRL, as some titles may be shipped in bulk.
In my opinion, it is well worth joining both, because they each have a different 'feel', and often present a slightly different point of view or emphasis on many topics. Radio is international by its nature, and I find it useful to know the interests and concerns of our British friends.