My understanding is you still hold the local bank's offer and have not made a decision yet? Honestly speaking, turning down the Big 4 Strategy offer was a huge mistake in my humble point of view. Here are (like all consulting answers) three reasons why:
1. The experience on paper you gain will be invaluable and will help you secure first-round interviews for MBB next year. This is because there is no guarantee that next year you will make it pass CV screening like you did for this year
2. The actual on-the-job skills will help you in your recruitment process (e.g. data analyses, graph interpretation, being concise in communication, time management etc.) because at the end of the day case interviews are supposed to be a simplified replication of actual consulting engagements
3. You have weekends + holidays + extra holidays (if you scale up) + sick leave to prepare in a given year. That, to me, is more than enough given you've already had initial preparation for this year's recruitment round
That's just my two cents on this. MBB is great but if you did get an opportunity for actual strategy work then I really think you should have taken it.