EPS to PDF conversion done by pdflatex is blurry

I suspect the shadowing uses PDF features, which are not available in PostScript. From the documentations, pgf-blur:

This effect can be achieved in TikZ/PGF with the circular drop shadow key,

And from the PGF manual:

In addition to the general shadow option, there exist special options like circular shadow. These can only (sensibly) be used with a special kind of path (for circular shadow, a circle) and, thus, they are not as general. The advantage is, however, that they are more visually pleasing since these shadows blend smoothly with the background. Note that these special shadows use fadings, which few printers will support.

Export the image as PDF and pdfTeX can include it directly without the need to run a converter for the down-graded PostScript file (the conversion is actually done by ghostscript).