I've jumped back into the Courier in preparation of the Engineers update - although I have no idea what is what and where is where but going to have a whole lot of fun finding things out!
The Vulture hits MUCH harder than Courier. First off, the DPS of weapons generally go up by 50% over the previous one. So three mediums is roughly equivalent to two large, BUT ... against large ships, two large does noticeably more hull damage than three mediums due to the drop off on most non-cannon weapons against ships larger than the hardpoints used against it. But more importantly, the Vulture has a class 5 power distributor compared to the class 3 of the Courier. So 41 vs 24 weapons capacitor, and 4.3 vs 2.8 weapons recharge rate. That's a HUGE difference in hitting power beyond the first 3 seconds of firing.
Vulture has a bit better base shield max charge, and MUCH better shield recharge rate due to the class difference and the strength of it's power distributor.
Don't get me wrong ... I LOVE the Courier and prefer it over the Vulture. But I do so because I love it's look, how she handles and sounds, and her modding potential in 2.1. But she in no way out DPSes a Vulture, ever.