Welcome Speedy!
AOPA and RAeS are 2 very different organisations. When I worked at Heathrow back in the 70's I joined the branch of the RAeS and massively enjoyed the lectures they put on in the Tech Block A canteen, given by such people as Jeffrey Quill, Alex Henshaw and Valentina Tereskova (the first woman in space). I've also enjoyed using their premises in Hamilton Place, London for meetings. I haven't kept up my RAeS membership as it no longer seems relevant for my position, not being able to get to branch meetings etc.
I'm a current personal member of AOPA and our Flying Club is a corporate member. As had been said above a few years ago, AOPA has an effective path to the regulator and regularly works to improve our terms and conditions. Mind you, EVERY group in the UK from the LAA to AOPA, the GA Alliance to APPG etc make the same claim. There have been numerous attempts over the years to get all the different groups to join forces but there has always been too many disparate vested interests for it to work out.
If you can only afford one membership (like me) and you're flying an 'EASA' aircraft, then my vote is for AOPA. If you're going to be flying a 'permit' type like a Jodel etc, then you'll probably need to join the LAA.
Ask AOPA about reciprocal membership in other countries.
TOO