The IBM brand in the UK/Europe deteriorated significantly over the last decade. The business model of IBM does not support a "real consultancy" division. Moreover, if you research portals like glassdoor.com you'll get a taste of what the motivation levels of IBM staff are and how this company treats its people. Therefore if you are looking forward to follow a career in the financial services industry BoA wins hands down any time of the day.
I have recently left IBM and the only regret I have is that I have overstayed. When it comes to SI full-service firms I would go only to Accenture, even though they are also following IBM’s path. From the Big 4, Deloitte seems to have a respected Tech division. However, as mentioned before I would any time of the day sign for a Bank rather than IBM or Accenture/Deloitte.
“Band 6” by the way, is quite low for an external hire. It clearly suggests they do not have any long term plans for you and that you are “just” an able chap who can do the job for 2-3 years before they chew you up and spit you out! No wonder, how some people manage to be Band 7, 8 or 9 for over 10 years...
This is well meant advice my friend!