I'm using the VariantAnnotation​ package and I want to intersect two VCF files to find overlapping variants. What's the most efficient way to achieve this?

I can intersect the coordinates of the two VCFs with the GenomicRanges::findOverlaps function, but I still want to make sure that the ALT fields of the intersected coordinates match. As these are ​represented by DNAStringSetLists it's not clear to me how to efficiently achieve this.

Not sure if it is the "best" way for you, but one way would be to coerce to a VRanges and use the ordinary match() functionality:

vr1 <- as(vcf1, "VRanges")
vr2 <- as(vcf2, "VRanges")
v1 %in% v2

etc

You might find VRanges generally useful for your use cases.