Burberry Sport is definitely the closest. I actually like it better because the citrus (grapefruit) is more tart and there is also even more ginger. Granted, like most Burberry's, it doesn't last that long (but neither does DHS). Also, I've started to see Burberry Sport discounted for $30 something or so at Marshalls/TJ. But, personally, I like Burberry Sport better than Dior Homme Sport because it's more harsh & biting.
Another you might check out is Tommy Bahama's Very Cool. It is citrus and Ginger as well, but the citrus is sweeter instead of sour in this one (it's mandarin orange instead of grapefruit and lemon). Very Cool is my favorite from the T Bahama line (and it's easily available for $19.99 for a 3.4 oz at all the discounters).
Another you might enjoy that is similar is Lacoste Essential Sport (the one with the blue juice). It's probably my sourest and most tart fragrance that I own (very realistic sharp grapefruit/lemon). And Lacoste uses a technology in their Essential line that extends the life of the top notes. I recommend this one as a very refreshing summer fragrance.
I like these kinds of really tart, sour citrus scents on summer days here in the southern U.S. where it is extremely hot (90 degrees F or so). I think they lend themselves perfectly to that kind of hot and humid weather. My go to scents on those kinds of days are YSL Live Jazz, Lacoste Essential Sport, Sean Jean I Am King, Burberry Sport, and Tommy Bahama Very Cool.