First lets put some descriptions in place of what data strategy is and what data architecture is? Strategy is an overused and vague term. The way I like to think of data strategy is the plan you put in place to generate more value from your data. This value comes in three ways: more income, less costs or peace of mind. Data architecture can also mean different things to different people. I would say it is the way in which different systems work together to support the data strategy.
From the data that is used to calculated the KPI's we know our customers so well that we can predict what different products will be in their shopping baskets and how we can reach similar prospects, providing an excellent customer experience along the way.
How your data architecture looks like, depends on the data you need to follow up on your strategy. That's why it is important to have a broad vision of where you want to go, and not just start using the data you have on hand.
The introduction of data driven decision making can be called transformational change, and will not be easy. For an organization to be able to react appropriately to the change of using data to drive decisions a certain culture has to be present.