Suppose a team of researchers sequences the genome and measures the proteome of a human skin cell and a human kidney cell. Will there be a greater difference between the genome or the proteome between these two cells?

There will be a huge difference in terms of size because a genome only consist of genes that code proteins while a proteome contains the whole map of all the proteins that'll arise from a single gene. For example, a skin cell genome is same as other somatic cell genome while a kidney cell proteome contains proteins like Angiotensin, Tomm - Horfall protein etc. All of these proteins may have risen from a single gene that'll ultimately make the proteome of kidney cells a number of times larger than that of genome of skin cells.

If you're asking about the genome only then remember there is no difference between the genome of somatic cells but a proteome always differs as the cell type changes.