The biggest difference with Chaos between the settings is scale and level of threat. In 40k, the Imperium is so massive that, despite what might be implied, Abbadon's black crusades aren't that dangerous to the Imperium as a whole. Yes, if Cadia falls, then Chaos will have a foothold for launching further attacks via a major, stable Warp path, and that's about it. Terra wasn't almost overrun, the Emperor wasn't almost cast down from the golden throne, nothing. In 40k, the Imperium can literally just keep throwing bodies at a problem until the attacker chokes.
In Fantasy, Chaos is a very real military threat to the Empire's very existence. The various marauder and Norsemen tribes actually outnumber the Empire by a good margin (don't have my Liber copies on the ship right now) and the only thing saving them is the fact that the tribes are fractured and divided. In 40k terms, it's how they describe Orks as being able to sweep the entire galaxy if they ever banded together. This is what make the Everchosen such a big deal - he's the Chaos Gods personal champion who can unite all the tribes and various factions together under one banner.
For a comparison of scale, imagine Abbadon launching a black crusade against the Sabbat worlds with an army big enough to attack every one of them. At once. And roll over the defenders in a matter of hours. Not months, years, or a decade. Hours. And then they keep going to the next set of worlds while driving straight towards Terra.
The Everchosen's invasions wipe out entire sections of the Empire. The only way the Empire survives is a) with the help of allies, usually Kislev, and also Dwarves and Elves, and b) by killing the Everchosen and letting the Chaos horde fight amongst itself.
On the small scale, it's the same. A chaos warrior is Fantasy's version of a space marine, except there are no good guys. Like if all the legions turned to Chaos and left only the Imperial guard to fight for the Emperor. So not only do they (possibly) out number you, they're also unstoppable killing machines.
Besides scale, the other major difference is motivation. The Chaos hordes don't attack the Empire because they're looking for revenge (some do, with Archon being a good example) they do it because it's a way to please their Gods and gain honor. They're not motivated by hatred as much as arrogance, seeing the Southmen as weak and soft. War is what they're born and bred for, they fight amongst themselves constantly and are always looking for someone else to fight and raid.
The characters are much better than most of the 40k ones. You have Galrauch, the 2-headed Chaos dragon that was originally a good dragon helping the High Elves until a Lord of Change possessed him. Sigvald, Slaanesh's spoiled little champion who's followers surround him with mirrored shields so he can watch himself fight. Aekold Helbrass, a Tzeentch champion who also creates life wherever he walks. Tons more if you can get some of the older books or the Liber Chaotica.