I can not comment about the differences in the two chips.

Have you used this v-reg before? This is one part you may want to breadboard. I looked at the data sheet and did not see a minimum voltage, are you sure the batteries are charged. Try putting a known load on the v-reg and watch the output. Could be something wrong with the v-reg or cap size.

It still might be a good idea to build an adapter and bread board the PIC. Try another power supply.

Just looking back to basics. To many variables going straight to finished product.