Then, I read the rules a little closer. They get furious charge, and the Mark of Khorne, which yields rage and counter-assault. This means +1S and +2A on the turn they charge. And if assaulted, they get +1A for the counter charge on a successful Ld check (which should happen most of the time ... but their Ld is now 8 though). Considering they come with a bolt pistol and close combat weapon, this means they get 4 S=5 attacks on the charge at WS=5. This is pretty decent. Until turn 2 in the melee when they revert to 2 S=4 attacks each (and 3 if they get assaulted in the interim). So they're strictly worse in the second round that they were in the previous codex, but on the charge, they're better and more brutal (not withstanding the loss of increased initiative to the furious charge rule). Does this balance out? Well, no: if you get the charge in, they're better full stop! So: get the charge in and do what these chaps are supposed to do: take skulls for the skull throne!
Points-wise, they're cheaper than they have been in the previous codex as well (effectively a free champion, and 2 points cheaper per marine), which makes them more appealing overall.
Let's have a look at their upgrades:
The chainaxe is appealing if we know we're not up against space marines (and other power armour Sv=3+ models). Otherwise, they're not worth it. Since the meta-game is so saturated with space marines and we're getting plenty of attacks, I suspect that we would forget about this upgrade most of the time (unless we've already modelled the chainaxes / fluffy reasons).
Swapping the bolt pistol for a plasma pistol is entertaining, but pricey. Ultimately, if the berzerkers are going to be charging high toughness targets, they're probably worthwhile (just). But try not to evaporate oneself in the process. (but wait: all blood is welcome, right?).
The Icon of Wrath grants furious charge (which is pointless, since the Khorne Berzerkers already get it), as well as the ability to re-roll charge distances. This latter ability is very useful, but probably not quite worth the points of the Icon.
Veterans of the Long War should be worthwhile if the local meta-game is indeed space marine saturated. And its price is very cheap!
The champion can take melta bombs (could be useful? at least situationally), the gift of mutation (if there's a spare few points around, but otherwise probably not needed), ranged weapons (a different way to get a third plasma pistol -- and therefore gunslinger by the letter of the rules; or perhaps a combi-weapon), and melee weapons (power weapons will be worthwhile, but I think a power fist might also be tempting -- but there's a real peril in the Champion of Chaos rule there).
Here's a couple of set-ups that might be worth exploring.
8 Khorne Berzerkers, 2 plasma pistols, Veterans of the Long War, Champion with Power Sword, plasma pistol and melta bombs, Rhino transport with combi-melta (280 points).
A compact unit taken in Khorne's sacred number with 3 plasma pistol toting marines transported in a rhino that is set-up to be a nuisance even without the berzerkers on board. Roll up the board and select the target. Get out and plasma pistol them. Next turn, get assaulted by (overwatch them!) or assault the targets. Should be case closed with a little planning.
10 Khorne Berzerkers, Veterans of the Long War, Champion with 2 Power Lances, Land Raider transport with dirge caster (475 points).
Use the land raider to get close, then assault. The double power lances on the champion are interesting: on the charge he will get 5 S=6 attacks with AP=3. That should be enough to take care of opposing characters. But feel free to swap out for more traditional lightning claws instead -- the lower strength is probably more than made up for by the re-rolls available -- I simply wanted to point out an innovation in double power lancing! And don't forget to apply the Dirge Caster's effects.