The differences among the two chips are the operating voltages, temperatures and some timings.
The DS28E02 reads and writes over 1.75V to 3.65V voltage range from -20°C to +85°C and has only 6-Lead TSOC and TDFN Packages.
The DS28E01 reads and writes over 2.8V to 5.25V from -40°C to +85°C and has the same packages as the DS28E02 but also an SFN and a TO-92 options.
The DS28E01 reads and writes over 2.8V to 5.25V from -40°C to +85°C and has the same packages as the DS28E02 but also an SFN and a TO-92 options.
Concerning the timing the DS28E01 and the DS28E02 have slightly different timing requirements in the twol parameter.
For the DS28E02 for overdrive is 8us min and 15.5us max and for the DS28E01 it is is 5us min and 15.5us max.
For the DS28E02 for overdrive is 8us min and 15.5us max and for the DS28E01 it is is 5us min and 15.5us max.