From my reading and you can do your own here. Sorry about the fact there are basically no studies comparing mealworm meal vs Black solider fly meal. In general, from my reading their doesn't seem to be much difference.
https://pubmed.ncbi.nlm.nih.gov/?term=black+soldier+fly+chicken
Most studies with black solider fly larva and hens are not using the larva as their source of protein, but as their source of fat, as even though they have many healthy benefits, they still are very fatty so make a great alternative fat option.
Studies looking at using black solider fly as a true protein source, "defatted" the larva and made it into meal, these studies are only done on boilers.
https://pubmed.ncbi.nlm.nih.gov/31062675/
https://pubmed.ncbi.nlm.nih.gov/30009465/
https://academic.oup.com/jee/article-abstract/111/4/1966/4990642?redirectedFrom=fulltext
As an alternative protein source there seemed to make little difference between BSF and other protein, though it is important to keep in find this isn't looking at long term effects, just metal levels, breast growth, and yellow fat level. Overall, unless the BSF protein can be sourced cheaper than fish protein there isn't much reason to switch it.
What I am finding in my research is that black solider fly is being recommended more than mealworms because a few reasons.
1. China has a better climate for mealworms so they are the ones that mass produce most of the mealworms found. The issue with this is the possible pathogens and bacteria that local chickens would be weak against.
2. Most mealworms found at stores are not dried properly, they are made hollow by the process and all nutritional benefit is lost.
3. Mealworms can only eat specific items, black solider fly larva can be fed and can thrive in almost any compost situation including manure.
In general, if you are making sure your mealworms or black solider fly are from a company properly drying them, or feeding live. And you are making sure they are locally sourced, then there really isn't going to be that much of a difference nutritionally. They also should not be a main food source unless you are doing broilers.