In my opinion, Target is actually a boutique store disguised as big box. It's that differentiation that'e kept them alive. There's less stores (you can find a Walmart in lots of towns < 10,000. Target doesn't bother unless you're talking > ~35,000 (and even in those cities there's probably 2 Walmarts to 1 at most Targets. They cater to a more refined crowd, thus the often differences in clientele. They carry higher quality/better designed home items and frequently change out their inventory. Yes I get that the actual quality of it is still questionable (particle board/polyester fillings) but it's still better designed for nearly the same price as a Walmart counterpart and much cheaper than you can find at an "actual" designer store. Their aisles are more pleasant and better designed. Though I think over the long run, Walmart just has too many stores and too much reach and Target will eventually be drowned out. Target's sales are getting crushed lately. Walmart has also started updating their stores and creating a cleaner look. They're also carrying better designer home products.
I was looking for patio furniture the other day and Walmart had better quality/price on all of the items I was looking for. This surprised me as I normally would've only considered Target but I checked both places. They had a directly comparable metal chair for $27 (Walmart) vs $55 (Target). And the table was metal vs wood and was much larger for only a few more dollars.
The main overarching issue for big box stores is the internet. People just don't want to drive or bike or walk around anymore to 10 different stores when they can go to one place that has pretty much everything for the best price and buy any super specialty items online. And as much as I dislike Walmart at times, they're winning in that regard by far.