Shield Cells alone won't help you kill stuff. Most small and medium hardpoint weapons suffer penalties when dealing with heavy armor. The Class 3 Pulse still eats through that.
Also, combat is more outmaneuvering than outgunning - and the Vulture does both (as soon as you kill heavier things than Adders anyway - which you can as well ram in a Vulture and be quicker about the kill than an Asp with weapons)
There's also only around half as much to hit on a Vulture - and it's agility comes in handy in both offence and defence.
For all-round purposes, the Asp is clearly the better vessel though.
Then again, for my personal kind of smuggly all-round, I prefer the Cobra simply because its top speed and boost are ace and I can spare two of the small hardpoints, utility slots and some cargo space when only doing smuggling missions, collecting assassination missions along the way to deal with after changing ships.
Had a blast smuggling rares in an Asp while hunting an occasional bounty though because the jump range is superb. But it's not exactly ideal to hunt and kill larger ships.
So, next to exploration, the Asp excells at armoured long-range trade/smuggling.
I'd like to see a decent Vulture pilot dogfight a decent pilot in a shieldless stealth Scout. Then again, the outcome might largely depend on whether or not the Vulture can adjust its outfitting for that particular match.