As noted by Virginia Postrel and others, Walmart is finally trying to make its stores more aesthetically pleasing. Nonetheless, I can't imagine that they will ever catch up to Target.
I remember when Walmart was new to the Twin Cities metro market. Walmart had been outstate for years, but they didn't start opening stores in the first ring suburbs until about the time we moved here in 1995.
At that time, there didn't seem to be much of a difference between the two stores. Walmart was closer than the nearest Target, and I never felt much reason to drive further for Target. In the intervening years, Target differentiated themselves, and we moved to another neighborhood. Again, Walmart is closer, but I nearly always pass it on my way to Target.
A big part of the difference in shopping experience is the design of the store. Customer service also plays a part. Line length at checkout is a big deal. Bigger than price, as far as I'm concerned. When a Target store has long checkout lines, I can tell that managers are trying to scramble to remedy the problem. I never get that sense at Walmart.
But the major difference is in product selection. Both stores will sell Swiss Army Knives, but Target will also sell the new styles of Leatherman knives, almost as quickly as REI will get them in stock. For all I know, Walmart has a couple Leatherman products, but I'm not really aware of them carrying the latest styles.
And then there's the design aspect of their private label merchandise. Walmart's knockoff products look cheaper than their brand name counterparts. Target's own brands (I can't call them knockoffs) often look better.
Most of the metro Target stores have undergone major upgrades in the past few years. Several of them were leveled and rebuilt. I'm fairly certain that Walmart has not upgraded any of their metro stores where I've shopped. I think only one Walmart in the metro was torn down and replaced, but I'm not really sure about that.
Target is building a new store near me -- at a location they upgraded in the last 8 years. They're building the new one next to the old one. In April, they'll close the old store, tear it down to make way for the new parking lot, and open in July. These people have more money than God, it seems. Okay, that's hyperbole, but from the way they act, one might think that they have more money than Walmart.
I live near St. Paul's Grand Avenue, one of the best retail streets in America. Okay, it's not Rodeo Drive, but its mix of specialty shops is excellent. I swear that the Target buyers cruise Grand Avenue and put the stuff they want in Target stores so they can buy it at a discount. Six or seven years ago, the kitchen gadgets at Target started to look like what I saw at the Bibelot Shop. More recently, the Target buyers must have all had babies, because now the preschool toy selection rivals Creative Kidstuff.
I've also noticed a difference in how Walmart and Target deal with out of season or discontinued merchandise (I'm not talking about clothing, but the other stuff). Target will mark it down steeply to make room for new merchandise. Often, they don't even wait for it to all clear out. After a few weeks, they'll donate what remains to Goodwill. Walmart, on the other hand, will mark prices down thirty percent and then let that stuff clog up the aisles for months.