This is simple: the ENRON scandal changed the world for consultants virtually around the globe. E&Y, KPMG (my old firm), PWC etc will stick to advisory work that they can present as being close to assurance. If they dabble too far into pure consultancy (as they did until three years ago), they get in hot water with 'auditor general' type government regulators. I lived through all this turmoil at KPMG.
These firms now do very little strategy consulting. If that's what you want to do (strategy) you need to shoot for pure consulting firms with no assurance affiliations today. AND, they too have found the world a colder place after ENRON, so their headcounts are generally a bit down on a few years ago, though picking up again. Also, many that did strategy and operational consulting have shrunk those practices to concentrate on lucrative, bigger demand areas like IT implementations and business process outsourcing.
In summary, if you want pure strategy, you won't find it at anything labelled 'Business Advisory Services' in a big five assurance firm. You also won't find much strategy work at KPMG anymore - the remnants of that were sold off with Bearing Point in North America and Atos Consulting in the UK. Would Business Advisory Work at EY prepare you for a bank? Probably. For pure strategy consulting work? Unlikely.