Advantages of A&A approximate to:
They try to do things properly, rather than compete on price. They aim never to have congestion on their network, and their prices tend to map directly to the wholesale costs of the products they're providing, rather than bundling things up in 'deals'.
They give customers as much direct access to their automated diagnostics and control systems as possible; you can run your own line tests.
Advanced diagnostics with pretty graphs mean you can tell the difference between, say, a line fault, something dodgy in BT's network or an upstream problem, rather than guessing.
IPv6, static IPs, various clever technical things you aren't likely to care about.
They're the first in line for sticking it to Theresa.
They have Shaun The BT Slayer, who will stop at nothing to kick our-favourite-telco into action over difficult line faults.
They're fully
xkcd://806 complaint, and are more than happy to communicate in whatever medium you prefer (SMS even, if necessary). If you say you've tested something, they'll believe you.
Lunar billing.
There's a cute cat on some of their documentation.
Disadvantages:
Cost
"Arnold who?"
They supply and support broadband (IP telephony, hosting, etc). They won't help fix your computer.