I have the newer AEBS with latest firmware. Have created a separate network for 2.4GHz and 5.0GHz both with WPA/WPA2 security.
Like I mentioned above, I've got 2 64GB wifi iPads. My wife has good connection throughout in the next room, while I get only 1 bar and disconnects frequently on both 2.4GHz and 5.0GHz. Even on auto network switching is unstable for me. The brightness trick does not work for me either.
What I can test is setting up a Guest Network to test.
UPDATE: Ok, I enabled Guest Network without security on my AEBS and I found out 2 things.
(1) Guest Network users connects directly to my AEBS. Seem like Guess Network does pass to my Airport Express (AE) if users are in my living room. When I connect to Guess Network from the living room the log shows me connect to AEBS not AE. Interesting...in a negative way.
(2) My problem was my iPad vs wife's iPad in our bedroom. Under Guest Network, I had constant full / 3-Bar signal for 10 mins where before under 2.4GHz / 5GHz network I would get 1 bar and frequently disconnects. My wife's iPad had full bars on 5GHz network during this test. I then forced my iPad to forget Guest Network and connect to 5GHz network. Immediately the signal dropped to 1 bar and frequent disconnects browsing and connecting to App Store. The same happened under 2.4GHz network. I then connected back to Guest Network and the signal went up and was able to browse and connect to App Store. Also on my Wi-Fi Networks screen shows that the Guest Network with no security had better signal vs my other networks with WPA/WPA2 security.
This could mean the security overhead is causing the problem BUT I have WPA/WPA2 at work and is fine throughout the office (2x bigger than my flat). However, my work is using a Linksys wifi router. So, the problem could very well be Apple's very own wifi routers (AEBS / AE) and the security overhead.