I would agree with Steven on the use of synthetic fluids for engine oil and transmission, however, not to sure that you would find ESSO as a brand readily available in the USA. It's sister companies are known as Exxon/Mobile over here and are part of the Imperial Petroleum Consortium.
As long as any fluid you pour into your Jaguars internals meets or exceeds the Jaguar specifications for your vehicle you should be fine. I have always used Castrol engine oil as it is made by British Petroleum and Jaguar specified and in both my XJ40s I use DEXRON IID TRANSMISSION fluid or an equivalent that meets Jaguar specifications. If you are at all confused refer to your drivers handbook
Best
David
