As a business analyst understanding a new domain should we look at the big picture or the details?
The answer is both. Each is a different perspective to give you a better understanding of the domain.
You need to understand the high-level business requirements to understand the why’s and understand the value the organization receives within the domain
You need to understand the details to make important decisions. It is the details that will reveal the good and bad decisions.
Start with the why’s then move to the what’s and then the how’s. Once you are understanding the how’s move back to the what’s and from the what’s back to the whys. Once things make sense in both directions you know you have a good grasp of the domain.