The Deluxe will have a Harrington & Richardson receiver, checkering on the laminated stock/forend and comes with a sling. They both will shoot the same but IMHO the Deluxe is worth the extra $43. The sling alone would probably cost you $20 - $25 and the checkered laminated stock/forend not only looks nice but are not as slippery in wintery weather. I have a 20ga NEF Ultra Slug Hunter LE (Limited Edition), it has camo laminated stocks w/medallion but no checkering and is a little slippery in snowy weather.
The gun shoots better than any slug gun I have ever owned over the past 30+ years, and I am talking about 1 Browning, 2 Remingtons, 2 Ithacas, 1 Mossberg and 1 SKB.
The USHD is still less expensive than any of the previously mentioned slug guns, even the one purchased 33 years ago.
Buy either one with confidence, they shoot excellent as long as you get a good trigger. Good luck.