PP tip, and opinions, please

This was shot through chain link fence.  Although I could "focus past" the fence, you'll see what it does to the background.

Many of the lenses we buy leave nasty little "edges" in the blur of our backgrounds.  To help fix this, I selected the background with a "brush tool" in CapNX2 (can be done in any PP program), and added some gaussian blur.  Note the difference.  The first is the processed image, the second is before I added the background blur.  Better image, after PP?