Thanks for your reply!
First, all of the VCF files are already decomposed. Second, I tried bedtools intersect before and it is not more sensitive. There is only one factor that determines the reported "intersected variant": which file was given first in the intersection. Meaning, running the command:
intersectBed -a A.vcf -b C.vcf | grep position
Will result:
chr position . C CT
But running the command:
intersectBed -a C.vcf -b A.vcf | grep position
Will result:
chr position . C CTTT
But I believe the correct result for the overlapping variant should be C->CT, without considering which file was given first.
BTW, I checked out intervene and it looks awesome!