Possibly, yes, but life wouldn't be nearly as different as someone would expect from a thousand year difference. Archaeologists and Egyptologists have noted a general trend of increasing religious "egalitarianism" from the Old Kingdom to the New Kingdom, wherein religious and death-related rituals that were once reserved for the pharaoh in the Old Kingdom were used by pretty much anyone with some money by the New Kingdom and Graeco-Roman period. From this its possible to assume a similar movement towards "equality" in other areas like government, but of course this is mostly speculation.

The real change in Egyptian social structure (which probably caused the greatest changes to the peasant class) was during the Intermediate Periods. Both of the dates you gave fall pretty firmly in the Old Kingdom and New Kingdom, times of great stability in Egypt. The Intermediate Periods, on the other hand, were characterized by destabilization of the central government. Destabilization usually means bad things for a country, and it probably made trade much more difficult, but it would have made taxing peasants more difficult as well. So living in an Intermediate period may not have been necessarily been better or worse for peasants, but it would definitely be different from living in one of Ancient Egypt's golden ages.