API 641 is Methane testing only
ISO 15848-1 is Helium or Methane. Purchaser is to specify.
API 641 temperature during test is measured at the packing, so valve experiences full temperature during test.
ISO 15848-1 test temperature is at the body. Packing area can be above the insulation and at a lower temperature. So the thermal cycle range is not as severe with ISO.
Test pressures are different between the standards depending upon the test gas and test temperature.
API 641 requires additional materials tests per API 622 for graphitic packing.
This covers the major differences.