List just the filenames from two buckets and diff them to see the difference
aws s3 ls s3://bucket-1 --recursive | awk '{$1=$2=$3=""; print $0}' | sed 's/^[ \t]*//' | sort > bucket_1_files
aws s3 ls s3://bucket-2 --recursive | awk '{$1=$2=$3=""; print $0}' | sed 's/^[ \t]*//' | sort > bucket_2_files
diff bucket_1_files bucket_2_files