Yes - sorry, you have a point that Basrah is much 'better' than Baghad but we only get to hear what the media want us to.
Basrah is not Baghdad. First, Basrah is far more ethnically homogeneous than Baghdad, so there is less sectarian strife in Basrah. Second, most residents of Basrah are Shiite. They were brutally repressed by the minority Sunnis during Saddam's reign. Consequently, they are far more favorably disposed to the current regime than the Sunnis.
Yes, Basrah is more stable and less dangerous than Baghdad. How much of that is due to the allegedly superior tactics of the Brits and how much of that is due to the nature of the populace in Basrah? I'd suggest that it is impossible to tell.