GATK hasn't changed a great deal in terms of math and calculations between 3.8 and 4, however there's been some significant enhancements under the hood in terms of speed and data structures. Variant calling is still a hotly contested topic, specifically filtering around what is truly variation and what isn't - see the blog post here which gives a nice comparison between Google's DeepVariant, GATK's VQSR methodology and GATK's still in development CNN. All in all, it's still an exciting area of development to keep an eye on.
So to get to the root of your question, I still feel that GATK's variant calling methodology is the gold standard to go off, but it certainly doesn't hurt to compare and contrast methodologies. I'd suggest you look at samtools / bcftools for an alternative approach which can sometimes be a great help when working with non-model organisms.