This solution assumes you selected a sensible 'ID' for your vcf files and used the same nomenclature/system in both files. It's not clear from your explanation but it sounds like you have one vcf for controls and one vcf for the experimental group. If my assumptions are not correct you'll have to add information to your question.

First, I make a file containing the identifiers seen in the controls:

cat controls.vcf | grep -v '^#' | cut -f3 > variants_found_in_controls.txt

Next, use this file for filtering the experimental group:

cat experimental.vcf | grep -w -v -f variants_found_in_controls.txt > variants_only_in_experimental.vcf