Is it more accurate to consider the Bitcoin network a data-intensive system due to the massive amount of data that must be stored by miners, or instead, a compute-intensive system due to the PoW and mining process?
This is probably one of those situations where any simple answer is inaccurate and misleading.
For any mining node, I expect computing costs much more than storage. By a long way.
For an individual non-mining node that doesn't use pruning, neither are really huge but maybe the data storage element dominates for at least some. Even so, the amount of data easily fits onto a single hard disk of the sort that can be bought at low cost. These are mass-market commodity items. It isn't at all like a large corporate data storage problem. It isn't Petabytes.
If you take the network as a whole, the data may become more significant since it is replicated on thousands of nodes but even so, it is the energy consumption of the computing part that is often compared to the energy usage of whole countries, not the data storage part.