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The capacity of each node (how many points it can hold before splitting) controls the shape of the tree. A low capacity means nodes split early, producing a deep tree with many small cells. A high capacity means nodes tolerate more points before splitting, producing a shallow tree with larger cells.
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The efficiency depends on the query size relative to the data distribution. A small query in a sparse region prunes almost everything. A query that covers the whole space prunes nothing (because every node overlaps), degenerating to a brute-force scan. The quadtree gives you the most benefit when your queries are spatially local, which is exactly the common case for map applications, game physics, and spatial databases.