I have created a vector graphic in Adobe Illustrator that uses a single brush stroke that has some rough brushed edges to the stroke. In between the miniscule brush strokes around the edge, it is transparent enough that it looks good when placed over any different color. In other words, in Illustrator, I can place the graphic in front of any colored background and it looks good.

However when I have imported the vector graphic (as a smart object) into Photoshop, it all looks great except the fine edges of that brush stroke is showing some "white edges" as if the fine transparency is not taking effect like it does in Illustrator. Any idea how I can get it to be fully transparent so these very detailed brush strokes allow the background colors to shine through at the very edges?? Thanks for your help.

You could try opening up a blank canvas in Photoshop andn then File>Place the Illustrator file. I don't know if it is possible yet to keep transparency between the two programs but that is worth a try. Have you tried to rasterize the image and then bringing it into Photoshop?