Same for those that vote for big endian 
A human readible format is not relevant for storing in EEPROM. It's only relevant for display purposes and hence your "dump" routine shoud take care of that.
But I guess that that ship has sailed 
@westfw already mentioned that networking is big endian; there are convenient functions / macros to convert. The implementation makes sure that whatever the input is, the output is big endian; same for te other way around, big endian input from the network will be converted to the correct endianness. Have a look at the functions in https://linux.die.net/man/3/htons.
Below is for 16bit, there are equivalents for 32bit.
If you use htons before storing, it will not matter on which processor your code runs; it will always store it in big endian in EEPROM. And your "dump" routine can display it.
If you use ntohs after reading it back, the processor will always get the correct format.