I agree with Matthew. Firstly there’s an uncertainty about his exact birthdate: the second newspaper article says 1852 but the obituary says 1850. If it was the former, then he would not appear on the 1851 census. Either way, it seems likely that the man was born on a farm near Bridgend, not Monmouthshire or Carmarthenshire (Bettws is a common place name in Wales and records have probably been conflated by overeager adding of sources on Ancestry).
I tried searching the GRO site for his birth certificate but (as was common practice) the middle name appears to have been adopted later in life, and almost all entries were for Griffith Griffith or Griffith Griffiths, making it difficult to work out which entry was correct.