Hi Rob,
I would guess that the probate records are more accurate because I'd like to hope that they'd be based on official records, such as the death certificate. The gravestone would be engraved from the information given by the relatives. However, both the death certificate and the relatives' information may have been handwritten and therefore subject to human error when read by others.
In short, probably neither can be absolutely relied on - probably best to get the death certificate.
Christine