I recently moved to Nashville and signed up for the AT&T gigabit offering which is 1Gbps up and down with unlimited data for $80 a month (what a deal).
Wireless devices cap out at around 400Mbps on Speedtest.net because they hit wireless throughput maximums. My iMac which is attached to my AirPort Time Capsule via CAT6 pushes around 700Mbps up and down. I'm fairly certain I am not being capped, just that Speedtest.net POP's probably can't push that much bandwidth to max out my 1Gbps connection.
I have a similar service (1gbps up/down) and I was able to get 944mbps by cabling my laptop directly to the ONT. According to my research, that's the practical maximum since there is some protocol overhead taking up part of the pipe. Once I reintroduced the router, I also dropped to ~750mbps.
Your contract with AT&T probably only guarantees you 70% of the advertised speed. I've never had an issue with speedtest.net POPs being able to handle gigabit tests. I have lots of experience with underperforming AT&T connections of all kinds. I would try another speed test site if you think that is the bottleneck.
@bigjimmyk3 brought up a great point. Most consumer routers can't push 1Gbps fully. Also, I am actually routing through two routers. The first being the AT&T supplied router/modem combo, then that flows into an Apple AirPort Time Capsule in bridge mode. All CAT6 cabling.
Wireless devices cap out at around 400Mbps on Speedtest.net because they hit wireless throughput maximums. My iMac which is attached to my AirPort Time Capsule via CAT6 pushes around 700Mbps up and down. I'm fairly certain I am not being capped, just that Speedtest.net POP's probably can't push that much bandwidth to max out my 1Gbps connection.