Microsatellites and Minisatellites: Which of these form the basis of DNA fingerprinting?
1) I'm told that VNTRs are used in DNA profiling. Does this refer to both minisatellites and microsatellites...or just minisatellites?

Actually, it refers mostly to STRs. I worked a bit in forensic genetics and we always published works using STRs markers (one example here, there are plenty in the literature). 

In addition, I would not be surprised if current forensic identification used SNPs instead, e.g. as proposed in this paper

2) If only one of them is used, why disregard the other? They're both (technically) VNTRs aren't they? So shouldn't either of them work just fine?

I really don't know, but I am sure that it has to do with one of a) level of variation, i.e. if minisatellites have lower mutation rates and are less variable, then they also are less useful, b) ease of genotyping. 

Browsing in the web I found this website from which I understand that the minisatellites were the first to be used to perform DNA profiling (using a method different from sequencing) and that "modern" DNA profiling is performed using STRs. However, I insist that modern DNA profiling should be better performed using SNPs.