I mostly Bh and occasionally explore. I never trade. The DBX is meant to be a bridge between smaller exploring ships and the Asp, and as this implies, it's better at combat then some cheaper exploring vessels (like the Adder, for example) and worse than some more combat oriented ones (e.g., the Viper). The DBS is supposed to fill a explorey-BH role, as in a BH capable ship with better jump and travel capabilities. While the DBX is very effective at its proposed role, the DBS is a little less so.
I've bought both. The DBS has decent maneuverability, being like a slower Viper. It's weapon setup is superior, mostly because of placement, but very similar, again, to a Viper. It's more resilient to damage then the latter, however. Personally, I favor more maneuverable ships for BH: the Vulture remains the best BH small ship by far, IMHO. The DBS is mostly meant for occasional BHunters.
The DBX, on the other hand, is an amazing exploring ship. Nothing comes even close at its price range and if you stock it with a Class A FSD, you get more jump range than with an Asp with a Class A FSD (32.5 unladden against 29.97 unladden), with the same fuel tank and for a much smaller price (you'd spend almost the double ammount of credits to outfit an Asp with a similar FSD). It is, in almost every way, the best small exploration vessel in the game. But, as a drawback, it's inferior to a fully outfitted Asp for exploration - the lack of a larger port for a 6A Fuel Scoop is a major one, as well as much worser capabilities for combat. While packing a little more firepower than some small ships - a large hardpoint makes a HUGE difference in combat - it's amazingly sluggish and lacks maneuverability against virtually every ship. I took several minutes to kill even SWs because I couldn't get them on my sight for more than a couple of seconds. Against groups, then, it's really a pain. All in all, it's a great exploring vessel - nothing more. The Asp can BH really well, on the other hand, and even with sub-optimal maneuverability, its weapon placements and sheer firepower make up for it. A Vulture is still better at BH, however.
TL;DR: The DBX is great at exploring, better than the Asp if you take the price into consideration. But don't expect it to fight well. The DBS does a better job at that, specially at it price range, but it's not the best combat ship you can get. You may buy one or the other eventually, but in the end we all end up in Asps, Pythons and Anacondas.
