For barrel longevity, it goes in this order.
A Chrome-moly steel barrel that the bore is chrome lined, then the Stainless steel barrel, then the Chrome-moly barrel that does not have a chrome lined Bore.
When your going for accuracy, the Chrome line plating can be cause variances in the bore (lands and grooves), so the SS barrel is a better choice. But in regards to a rifle that is going to heat the hell out of a barrel (read M-16) a SS barrel will pretzel, so on the M-16, SS is not a option, and the chrome plated Bore is used to prolong the barrel from plasma throat erosion.
Now a primer on barrels, a barrel starts its life off as a rifled blank (round tube of steel). This blank is then turned into a working barrel by profiling and chambering, then bore plating if chrome lined.
A barrel blank is just the first step, it's the production of the blank that will either determine if the barrel will be accurate or not. So before you put a lot of stock in the brand name of a barrel blank type, hence Wilson or Shaw, find out who is turning the blank into a finish barrel, and if they will guarantee that there finished product/barrel will group or not.