Might be of some use:
http://www.lpl.arizona.edu/impacteffects/Most comets do in fact orbit with higher velocity than asteroids, especially the long-period ones that swing in from the Oort Cloud. The above link says average impact velocities for asteroids are 17km/s, while comets can be mighty speedy at 51 km/s.

Running a quick simulation with typical values for a comet impacting land (6km diameter object consisting of ice, impacting at 51km/s on sedimentary rock), we get the following: (Calculated with observer 300km from impact)
Energy before atmospheric entry: 1.47 x 10^23 Joules = 3.51 x 10^7 MegaTons TNT
Transient Crater Diameter: 48.1 km = 29.8 miles
Transient Crater Depth: 17 km = 10.6 miles
Final Crater Diameter: 80 km = 49.7 miles
Final Crater Depth: 1.11 km = 0.687 miles
The crater formed is a complex crater.
The volume of the target melted or vaporized is 920 km^3 = 221 miles^3
Roughly half the melt remains in the crater , where its average thickness is 507 meters = 1660 feet
Visible fireball radius: 98.3 km = 61 miles
The fireball appears 74.5 times larger than the sun
Duration of Irradiation: 1370 seconds
Radiant flux (relative to the sun): 518
The major seismic shaking will arrive at approximately 60 seconds.
Richter Scale Magnitude: 9.7 (This is greater than any earthquake in recorded history)
The ejecta will arrive approximately 254 seconds after the impact.
Average Ejecta Thickness: 1.76 m = 5.79 ft
Mean Fragment Diameter: 2.92 cm = 1.15 inches
The air blast will arrive at approximately 909 seconds.
Peak Overpressure: 853000 Pa = 8.53 bars = 121 psi
Max wind velocity: 697 m/s = 1560 mph
An impact of this sort would indeed be catastrophic, killing anyone within several hundred miles of the impact site within moments. You ask more specifically for long-term climatic effects, and this is significantly more sketchy. I'm by no means an expert on the subject but I'd imagine a great deal of extinction would occur from the disruption of photosynthesis due to ejected material blocking out sunlight, and global temperatures would most likely drop a significant amount. How long and how severe this would be I do not know. But I do expect life would survive at least on some level, and here you have a lot of freedom for your fictional setting. Humanity, assuming it survives, would definitely see a drastic change in its customs. We might function on a more isolated and tribal level, or perhaps we'd attempt to wait out the environmental chaos by living underground and growing our own food somehow. Just some ideas to consider anyway.

Edit: Oop, Kara beat me to it.
