Like everything else in aviation, it comes down to mission. The EAA is for the experimentals and the AOPA is for the TSO'd and STC'd.
Many belong to both, but if your aviation dollar is constrained, then join EAA if you are a dreamer and AOPA if you own a plane.
Don't misunderstand my meaning of dreamer, the EAA gives people who just love flying with minimal constraint the chance to spread their wings, even if they never build a plane. The AOPA is a bit more formal, more corporate and it does cater to aircraft owners of the certified kind.
I belong to AOPA and use it's bennies regularly. I find no use for EAA personally and my extra "joining money" goes to MAPA.
Wrong wrong wrong.
The EAA is for aviation enthusiasts.
AOPA is for people who like to waste money on an organization that spends more on recruiting members than it does on "advocating" for GA.
When I was a member of AOPA, I was more heavily recruited to join than anytime before or after. I calculated it, and found that they actually spent more money on recruiting me than I was paying in dues. And that is not including the materials I received to contribute to various PACs.
AOPA is a soft organization that does not really stand for anything anymore.
The EAA, on the other hand, stands for something. They promote aviation by holding a large fly in that is available to the public and they offer discounted (or free, I can't remember) admission to EAA members that arrive via airplane.
Does Sun n' Fun do anything like that?
The EAA provides local meetings for pilots to group together and talk about aviation. They usually meet at least monthly.
How often does AOPA have a meeting in your area?
The EAA supports all forms of recreational aviation, from experimental to LSA to Twins, and even bigger, as long as its used for fun.
AOPA supports bizjets and Cirrus/Columbia drivers.
EAA supports CFIs by giving clinics and great amount of information to members to learn from.
AOPA has a "Student/CFI" magazine that rehashes stories every 6 months or so.
What does AOPA have that EAA doesn't? Well, an insurance plan that is generally not discounted compared to non AOPA plan pricing. Discounts on cars that actually cost more than not using the AOPA plan numbers. An airport directory that is about a year outdated by the time it arrives in your mailbox.
In truth, the only real reason to pick an organization, however, is not to get stuff. It is because that organization is actively trying to defend GA to the public. AOPA takes credit for others' work. EAA gets stuff done.
And that is the long and short of it.