The Viper is faster and has more powerful vertical and lateral thrusters.
The Vulture turns much more quickly, has incredibly strong shields, and can mount class 3 weapons which are much more effective against large ships like Anacondas and Pythons.
The Vulture is also very tight for power (even more than the Viper), even with just basic class 3 pulse lasers you will struggle to fit a full set of A-grade internals without compromising something.
That said, the difference between the Vulture and the Viper is night-and-day when it comes to killing large high-value NPCs. The Vulture has the shields to go toe to toe with them safely for long enough to smash down their shields and kill their power plants, resulting in safe, efficient earnings in Extraction Sites and Combat Zones. Also, because it can get enough armour penetration to kill large NPCs without having to use kinetic weapons, you can just stay in a RES or combat zone and blast away until you've had enough, without needing to re-arm.
Think I spent about 16 million all-in on mine, and I don't feel like there's any NPC encounter that can threaten it. Won against three Master+ Anacondas at once in an SSS yesterday after my wingmate in his Cobra got chased off almost immediately. Came out of it with no shield cells left, but not a scratch on the hull.
Can't say much as to PvP as I haven't fought another commander in it yet.
Try playing around with shield boosters in EdShipyard. You may find it is just as tough and quite a bit cheaper if you downgrade the shield generator and put a couple of boosters on.
Edit: also, the cockpit view in the Vulture is a little restrictive compared to the Viper, there are these two whacking great armour plates that block your view out of the bottom right and left of the canopy. It's not that big of a deal as the hardpoints are on its "shoulders", so your target should be slightly above you anyway if you're using gimballed weapons.