The White Scars are a Chapter that specializes in lightning raids and hit and run warfare, often fielding armies dominated by bike squads. Their Chapter Tactics do a great job of representing this on the table. Their bikes ignore Dangerous Terrain and gain +1 to their Jink saves (basically Skilled Rider under another name, which is great if you can come up with a way to give them Skilled Rider on top of that). Beyond that, they have +1 strength to their Hammer of Wrath hits. It won’t turn Space Marine Bikers into a real assault force, but every bit helps.
For those of you that aren’t into bikes, the White Scars have something for you too. All of their models save for Terminators and Centurions have Hit and Run. Do you miss the old Combat Tactics allowing you to break away from combat? White Scars do it even more reliably than before. This is a massive rule for most Space Marine units, as they don’t want to be locking into assault; this allows them to fall back and keep pouring fire onto the enemy.
The White Scar tactics lend themselves well to bike heavy armies, doing them arguably better than Ravenwing. Even so, their other rules greatly benefit most other Space Marine units, meaning that you can take a well-rounded White Scars army without wasting the benefits.
Kor’sarro Khan is the Captain of the White Scars 3rd Company and the Master of the Hunt. He’s a very standard Captain, though he has a power sword that inflicts Instant Death on a 6 to wound. Just like for the Executioners, it’s a handy ability when it works but it won’t allow Khan to deal with real combat monsters. Khan can (and probably should, in most circumstances) ride his bike, Moondrakken, which inflicts D3 Hammer of Wrath hits when he charges. He has the Champion of Humanity trait, which as discussed previously, can be game winning but is hard to implement.
Like most good special characters, the reason to take Khan is his effect on the army as a whole. All White Scars with bikes or dedicated transports gain Scout. This will allow you to redeploy and outmaneuver your enemy, or just to get in their face in the first turn. While it won’t allow you to launch first turn assaults, it will get you into range to blast away at the enemy with all the grav guns that Space Marine Bikers seem to be carrying lately. If you want to be sneakier, some of your squads can Outflank to reach backfield objectives.
Kor’sarro Khan is a great choice for an aggressive list. He’s not as damaging or resilient as a generic bike character can be, but he brings great options to your entire army for an extremely reasonable cost.
If you're really interested in the White Scars, I suggest looking at the Mongols they're based on for inspiration. An excellent overview (if you have the time) is the Wrath of the Khans series from the Hardcore History Podcast.