Is chromosomal DNA more likely to interfere with restriction mapping or PCR analysis in E. coli?
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I think you've come to a reasonable conclusion, but not for exactly the right reasons.

The genomes of several strains of Escherichia coli have been sequenced (e.g. https://www.ncbi.nlm.nih.gov/nuccore/U00096) so you could predict the sizes of the fragments you would expect from your digest. 

The genome size of E. coli is about 4.6 million base pairs and six-cutters like EcoRI and BamHI cut on average about once every 4096 bp (you should be able to figure out how to come up with that number). From that what would you expect to see if you did a restriction digest on this bacteria's genomic DNA?

Does that help you improve your answer?

(If you have access to the appropriate software, I encourage you to download that sequence and check your conclusions.)

((Also note that the specificity of PCR is dependent on primer selection, so your answer is assuming that the primers were well designed!))