There is some debate about which of the two - Egyptian civilisation and Sumerian civilisation (Mesopotamian) - is the oldest. According to my knowledge relating to the orthodox view, Sumeria is the oldest civilisation at a date of 4000BC, but according to other experts Egypt was the first truly organised civilisation albeit not as old as the Sumerian.
One group of experts suggest that ancient Egypt is much older than we think, and that the chronological timeline of Egyptian history from the reference point of the first Dynasty c. 32-3100BC (sourced in Manetho's histories, and the various kinglists from temples and tombs) may be biased and incorrect. Indeed some Egyptologists have pushed back Egyptian history much further to about 6000BC neck-and-neck with the rise of Sumerian civilisation.
Some experts prefer to see Egyptian civilisation in separate parts relating to periods of "cultures", such as the "Sudanese Civilisation", the Kerma culture. But I doubt whether the Kerma culture is truly ancient.
Because no-one can come up with a satisfactory answer as to who, out of Sumeria and Egypt, is the oldest civilisation, I believe that the two started their civilisations at about the same time, except that Egypt was perhaps more organised than their Sumerian brothers.
For Sumeria I would posit a date of 3800BC for the rise of its civilisation alongside the Tigris and Euphrates; for Egypt I would posit a date of 5000BC - a predynastic civilisation that begun in the savanah along the Wadis.
Of course, it is very possible that there were older civilisations (older than Sumeria and Egypt) still yet undiscovered. As for the oldest civilisation in Europe? I would guess that we have not yet found it, but I think Germany might be a good place to start.
What do you think? Which of the two is more older? Egyptian or Sumerian?