i'm honestly not sure what you mean by "store brand" vs. "specialty". i choose my lubricant based on it's ingredients and manufacturing. The brand name factors in only so far as knowing that particular manufacturer is responsible and reliable in their production and business practices. It's not that it's "specialty" lube. It's that it's conscientiously produced with safe, reliable ingredients using safe, eco-friendly manufacturing. If there was another brand that lived up to my expectations in these areas, i'd have to compare other factors. So far there isn't.

I am referring to store brands such as Walgreens Personal Lubricating Jelly v. brands such as Id Glide and others sold here. I've used both and don't really see a difference in quality, however there does seem to be a difference in price. I can see that if you have a reaction to chemicals in lubes, why you would be careful about the ingredients but if not, are there other considerations I am unaware of?

cheap and generic don't always equal quality.

There is a difference!

As a strict rule, i won't use lubricants that include glycerin or parabens (such as methylparaben). The list of ingredients in your post above includes both. Glycerin can cause a lot of common vaginal issues and parabens are linked to cancers and other problems and i also try to stick with lubes that are natural and organic to avoid harsh chemicals and potential allergens. i used to use ID Glide, not because i liked it but because it was what i was used to. i wouldn't consider anything in the ID line "specialty". When i started learning about ingredients and potential problems and when i developed a series of infections from lubricants, i switched to YES lube which is a bit on the pricey side, especially with shipping since it can't be ordered from EF or any other US company and has to be shipped from Europe, but i find it to be well worth the price. Sliquid is the only other brand i know of that i would seriously consider.
i can definitely say that my YES lube is a far cry superior in texture and performance compared to ID glide. i've never used anything like Walgreens brand but i'd hazard a guess that YES is a vast improvement. i can't vouch for Sliquid because i haven't actually personally tried it.

If by "store brand" you mean something like walgreens or equate, then yes, there's a huge difference. If you mean something like Sliquid vs Babelube, then no, not really. At the same time, a good portion of lubes you get at walgreens, walmart, or wherever else are loaded with glycerin and other chemicals that can mess up your pH and give you a UTI.

Store brand I find is much lesser quality than what I can find on Eden.