I don't have Persian Accents , but I do have a couple of the new lighter colored dies. I laid the shaft of a sewing pin next to the ridges to measured the depth on the older ones and the newer ones and you are right!
The ridge is not as deep on the newer ones.
I think it is the new paint they are using. The old paint must have been thinner and left a sharper ridge. The new paint collects a bit at the base of the ridge and makes it slightly more shallow.
However, mine are cutting. I have the new Edgeabilities Classic Petal which is quite intricate. It cut in one pass with my Cuttlebug and no extra shims.
I use the A (base) --B plate--Cardstock ( Georgia Pacific) Die-- C plate and ran it through.
In my haste to try it I forgot to put wax paper between the CS and the die and spent a lot of time with a tooth pick pushing out the parts left in the die