To change the background color, go to the Property inspector and choose different background colors to see how the edge of your ring looks against them. Notice that the edge of the ring does get anti-aliased correctly to each new background color. This was definitely not the case using the old-fashioned method. The difference in the quality of the results between both methods is quite significant. Moreover, with vector masks such as this one, the process is never irreversible; the mask remains editable at all times. Because you deleted no pixels in the ring image, you can still tweak the vector shape and try to get better results.
For example, there are two areas which I think should be tweaked (see Figure 7). If you zoom closer to the image you'll clearly see why. Look at the Areas That Need Editing layer in the Diamond_Ring_Mask_final.png file and zoom to about 400%. On the left, notice how the original selection did not closely follow the inside curve of the ring. The problem is even more obvious in the right area where the point doesn't go far enough to the right and the curve at the bottom doesn't closely follow the curve of the ring—leaving a strip of white that looks out of place against the contrasting black background.
Figure 7. Two areas that need a little work
Moving the rightmost anchor one pixel to the right and editing its curve handles solves the problem. A little tweaking of the position and handles of the anchors in the left area also fixes the curve in no time (see Figure 8).
Figure 8. Final result after tweaking the mask
If you wanted to be picky, you could also edit the vector mask path around the diamond itself where the mask has left a few white areas. It looks pretty good as is, but you could always edit it by hiding or revealing parts of the underlying image until you are satisfied. This is something that is simply not possible using the old-fashioned method because the pixels that are gone are gone for good. The only thing you could do is remove more pixels.