How does the use of molecular data such as DNA and protein sequences compare to the use of anatomical evidence? What are the pros and cons of each type of evidence?

There are different evidences for evolution that includes anatomy, fossils, molecular biology and biogeography.

Molecular biology uses DNA and protein sequences that the genetic code reflect the shared ancestry of life. DNA comparisons used for the anatomical evidence.

All living cells are organized in the same basic DNA and use the same genetic code. Proteins derived from genes, all originate from the same set of amino acids.  Comparing parts of DNA in various species has shown that even very different organisms still have significant parts of similar DNA. For example, in chimpanzees and humans have some precent of same genetic structure. In the amino chain, chimpanzees and humans have only one position, while humans and moths have 31 different positions.

There are different advantages and disadvatages of each type of evidences are:

Advantages:

Anatomy share information about the similar physical structures shared by common ancestor (homologous structures)Fossils provide information about the extinct species.Molecular biology provide genetical relationship between organisms.Biogeography share global organism distribution and island species unique characteristics reflect evolution and geologic change.

Disadvantages:

some of the structures such as forelimbs of human and birds seems homologous in structure as per comparative anatomy but they  have evolved independently in each species.Fossils are impressions of past living organism and buried in earth surface rom long geological past, hence during this geological time there can be many changes in the fossil structure and can manipulate the evidences.Molecular biology has disadvantage of lack of assay specificity and sensitivity.organism can evolve and adapt according to different condition, hence Biogeography can not exactly tell the exact changes in the characteristics of organisms on the basis of particular geology.

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