Around 10 years ago, DL put a lot of effort into actually delivering priority bags first, and it generally worked. I'd say at least 90% of the time I checked a bag, the priority tagged bags showed up at the belt first. (There were of course exceptions, and some stations were better than others.) This was a separate effort from the "Bags On Time" guarantee mentioned upthread, which is no longer advertised but still works - 2500 miles immediately applied to your account if you fill out the form and are eligible, regardless of cabin/priority tags.

Interestingly, in both cases IT plays a key role in service delivery (along with staff training and other aspects, obviously). Priority bags are actually coded as such on the bag tag itself (the yellow tags serve as a visual indicator, but are not otherwise particularly functional), and the Bags On Time guarantee is implemented by simply comparing when the plane arrived and when the bag was scanned as being delivered to the belt (so usually a minute or so before you actually receive it).