ASL offers the American programme throughout the school. It is very difficult to gain entry into and is the most sought after international school in London. Its admissions policy is slightly bizarre because it is a mixed ability school so the "top" candidates are not necessarily selected but there also seems to be no clear indication as to why one student will be selected over another. Factors like siblings at the school, company the family are being relocated by, etc, tend to play a role but they keep their reasons for selection to themselves. Politics plays a role no doubt, especially as it is a non-profit school and they have big donors.
Southbank offers a totally different curriculum - the IB, which is no less or better then the American programme, just different, so it's really a matter of personal choice. The Diploma Programme of the IB (16-18 years), however, is generally considered more rigorous and challenging than the American High School Diploma (even when taking into account the Advanced Placement (AP) programme). Some of the more selective British schools now offer the IB Diploma alongside A Levels, and tend to usher their stronger students towards the IB, as the more 'elite' universities tend to select IB Diploma students with a strong diploma score over students with strong A Level scores.
ACS Hillingdon offers an integrated curriculum in their Primary School (i.e. American, Primary Years Programme of the IB, and British National Curriculum), the Middle Years Programme of the IB in their Middle School and a choice of either the IB Diploma or American High School Diploma at High School - they tend to 'encourage' their more able students to pursue the IB and their 'weaker' students towards the American High School Diploma. In a way, they offer greater choice at the High School level than either Southbank or ASL, and the best of both worlds.
In terms of the 'hierarchy' of the three schools you refer to, ASL is #1. ASL are considered 'leaders' in the world of international education and with good reason. Everything from the quality of their teachers to curriculum and leadership is strong. It is not just difficult for a student to gain entry but also for teachers to land teaching roles! It is non-profit so there are no 'compromises' in terms of quality. Their results are strong across the board. Read the latest Ofsted report - it is glowing.
Southbank is considered a very good school but it is considered "ASL's car park" and even their staff members attest to this statement. Many students attend Southbank as they wait for places to become available at ASL. Southbank is profit run - part of the Cognita group - so there are lot of compromises for the sake of profit (Cognita is a subdivision of a private equity firm). It is very selective at Diploma Programme level so they have a strong record at this stage of the IB. The school was in the press a few years ago due to unrest amongst the parent body about Cognita's management of the school. Parents have since started their own non-profit IB school, as they claimed that Cognita had changed the heart of the IB at Southbank and were trying to turn it into a British school. Many families and staff members have left since Cognita took over...
ACS Hillingdon is also a profit run school but is run 'more ethically' than Southbank. They are transparent about their profits. If ACS was based in central London, it is likely that ASL would have strong competition but their location in the suburbs (albeit a stunning campus) is the primary reason families tend to choose ASL (ASL is more central). The morale at ACS is strong amongst both staff and families so that speaks volume about the experience for both students and staff.
I hope the above provides a good starting point for your decision. Am happy to answer any further questions if you require further information.