Intuition behind recurrences with growth O(n log n) vs O(n²)
What you are missing is the big O constants. In the first case, at successive heights you are doing work of $$n, 2\frac{n}{2}, 4\frac{n}{4}, \ldots = n,n,n,\ldots. $$ In the second case, at successive heights you are doing work of $$n^2,2\frac{n^2}{4}, 4\frac{n^2}{16}, \ldots = n^2,\frac{n^2}{2},\frac{n^2}{4}.$$ Since the series $1,1/2,1/4,\ldots$ converges, the total work is only $O(n^2)$.