Does the possible speed achieved actually vary between the providers, or is it like re-sellers of power, the same "power" coming down the line just different rates charged by providers?
Yes and no: With the exception of Virgin cable, which has its own physical network, ISPs buy one of a handful of wholesale products from BT and a couple of other providers in order to connect your modem to their servers. From there, the onward connection to the internet is up to the ISP, but in practice this is rarely the bottleneck. The main difference between ISPs comes down to pricing structure, ancillary services such as email and web hosting, how much they dick about with your connectivity to the outside world (DNS hijacking, porn filtering, download throttling, provision of IPv6 connectivity, and so on), and crucially, how competent they are at dealing with their wholesale providers when there's a fault.
What wholesale products are available will depend on your exchange, cabinet and so on. If FTTC is an option it will usually outperform ADSL2+ by a healthy margin. Virgin cable performs well, but limits you to Virgin as an ISP.