I recently bought a DB Explorer and kitted it out pretty much all A-grade, though I haven't had a chance to take it on a long trip yet.
I sold my Asp so I could afford a Python, but I'd say the DBE compares very favourably, at least on the stats.
It's a bit smaller, with fewer module and hardpoint slots, and (I think) a smaller fuel tank, but fully armed and kitted out, it still has a 29 LY jump range (I think my Asp was 27 LY, but I don't travel without weapons, so since the Asp is bristling with them, dropping them would probably increase the range significantly.
The DBE has a lovely feel to it too, but sounds weird when you're decelerating after a boost.
The Asp has a slot for a HUGE fuel scoop, so you don't even need to decelerate to scoop, but the DBE uses less fuel (being lighter) so a 4A does the job just fine.
Fully outfitted for exploring, unlike the Asp, the DBE has no room for even a small cargo bay (I like to keep the option of picking up something interesting if I find it), but that's not why you're going out into the big black yonder, is it?
The power management and heat management on a properly outfitted DBE is excellent too. You can't have all A-grade, but pretty close (I don't have anything below a C).
You need to watch your heat in an Asp. Not in a DBE (but pack some heat sinks anyway).
Happy exploring!