The reality is that there is not much difference between ACCA and CIMA. You can do almost exactly the same exams and both are relatively flexible in work experience - I qualified as ACCA working in industry doing a combination corporate strategy, M&A and finance/performance management jobs. I am now working in FS doing strategy and mgt consulting.
While the qualification has helped, the work experience was probably more valuable. Spending 3 years producing internal MI reports with CIMA would have been far less useful, and audit work with either ACCA or ACA accounting firms would not have been so interesting. Consultancies will like an accounting qualification, but unless you want to do Finance function work, you should also focus on getting relevant commercial experience within a good company.
I don't work in MBBB, so not sure if this route would help you if that is your goal (although I suspect it would not from reading other posts).