The reason is that no other ISP, other than Be, has access to your actual Be performance data, so they are all forced to rely on BT's unreliable database, which you can see yourself at: BT BROADBAND AVAILABILITY CHECKER
on BT's network the speed I can get is around 6MB, whereas with BE I can get 12MB.
Are you say you actually got 6 Meg from BT or that BT estimates your line at 6 Meg? If the former you must have been on 20CN ADSL Max. Perhaps BT doesn't have 21CN WBC ADSL2+ at your exchange but Be does have LLU ADSL2+. What exchange?
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC