Here's my 2 cents. Any food regardless of it origins or ingredients can be considered healthy with the exception of a trans fat. Basically healthy is a red herring. The problem arises when people try and advocate one over the other like this example. Non vegans and lacto ovo vegetarians have the option of using either, while vegans don't, and that's where the complication and comparisons begin on one being healthier than the other. Unfortunately in my opinion the vegan associations that had a voice tried to paint animal foods as unhealthy which I think was a bad strategy but in hindsight probably were only left with health comparisons to drive their platform.
What does healthier mean? In this example it's clear that animal dairy is said to be healthier and for all intense and purpose it is as far as a nutritional profile is concerned. This doesn't make almond milk et al unhealthy because like I said all food is healthy. It comes down to a choice for the individual to decide which foods they make for their particular diet and if it has all the essential nutrients and a person can thrive, then what's the problem, right?
The issue for me is in the reluctance of accepting any shortfall for essential nutrients. For example omega 3's from animal products. Vegans will argue that omega 3's from plants are sufficient. I argue from a science point of view that they are not. Omega 3's in animal has the essential nutrients of EPA (eicosapentaenoic acid) and DHA (docosahexaenoic acid} while plant omega 3 have what's called ALA (alpha-linolenic acid) which is not essential. Theses are not biologically equivalent and the ALA needs to be converted first to EPA which the body can do and will do in the absence of EPA. The conversion rate is very low, less than 1% on average. To complicate things further the converted EPA is then converted further into some DHA the other essential fatty acid. There is an algae based supplement for DHA but it's costly and quite a bit is prescribed daily and it also lowers the ratio of HDL and LDL cholesterol, which would increase with consuming fish for example, which confusingly, is better.
As far as health in general goes the balance between omega 3's and omega 6's should fall into the 4:1 to 1:1 ratio depending on which medical journal your reading for optimal health. In the USA that ratio is anywhere from 12:1 to 25:1 depending on the percentile a group of people fall into. Omega 6's are basically plant omega's and seed oils are the most prevalent in the diet. The importance of the ratio is to balance inflammation with omega 3's anti-inflammatory with omega 6's inflammatory. A health concern for decades.