I used AOPA's insurance for my rental pilot policies and I was happy with their service and price. Fortunately I do not know how they are about handling claims.
When I bought the AA1B their prices were much higher than the agency referenced by AYA so I no longer use AOPA's insurance.
Part of it depends on your qualifications and aircraft; for instance, one the A-36 and the Baron, Falcon works with ABS and has done very well for me. Also, other owners have given me great perspective. On experimentals, others seem to do much better. AOPA wasn't very competitive for me and my planes; perhaps it's the broker I was in touch with. EAA wouldn't be attractive for my situation either, but fits some of my friends with things like an RV very well.