Sleijpen and Van der Vorst 1996 estimate the computation costs of direct methods as N^2.3 with memory costs N^1.7, while iterative methods yield N^1.2 and N^1 respectively for N by N systems (tested for three-dimensional elliptic boundary-value problems).
Now direct methods always have some black-box and are generally not suited for large sparse matrices. I really cannot answer why your system gives you better division costs. However, I saved the following flowchart from one of my courses. It is on the last page of http://www.netlib.org/templates/templates.pdf .
For instance, cgs is for non symmetric matrices where the transpose is not available and you have little memory. If division is still faster and you find out why, let me know; strangely I find it really interesting.
