Fluorescent light above still life with no diffuser:
The shadows are quite harsh here, this was made in purpose to more easily see the effect of the diffuser in the next shot.
With white translucent diffuser:
Although the diffuser hasn't "killed" all the shadows it did a good job at redcuing and softening them. When looking at the shadow of the string holding the flintstone we notice quite a difference with the previous shot. The shadow is much more faded. More details are now visible in dark areas. I suppose a greater distance to the light soure would help removing the shadows.
I like the softened picture more as the shadows in the first shot are aggressive and don't really add value to the picture. However, I can see how both approach could be used creatively depending on the scenario. Knowing that, I also understand that in some situations it would be unaceptable having any kind of shadow and a diffuser is inevitable in some cases.