Zarathur's control is almost entirely damage based, and he hates to have to spend big (in cards or resources) to achieve that control. Zarathur/DE can access Archon's Terror, but I'm of the firm belief that Zarathur and Ammo Depot is such a strong combo that orks are the best allies.
He's at his best when he can use one card to take out multiple cards, like a Plaguebeast or Warpstorm, or even a Flamers that attacks then sacrifices.
He's at his worst when he has to use multiple cards or a lot of resources to take out a single target. HP-Resilient units are his nightmare.
Playing as Zarathur I've often had to bite the bullet and throw big ass Firestorms at a Shrieking Harpy or a Land Raider, simply because I have no other option. This is always, always painful.
Cato is also a hard match up. While sacrificing doesn't trigger his warlord ability, there's a tendency for him to present a small number of good units in a fight, and to have just the right number of shields to save them from destruction. Also, surprise units can result in a bloodied Zarathur, which makes it hard to risk attacking with Flamers before sacrificing. Also, Zaraswarm (the best Zara archetype, in my mind) is happiest when using Ammo Depots for draw and hammering Osus and similar planets for the resources. This means that to play its own ideal game, it has to let Cato play HIS ideal game, which is dominating command at Elouith and pulling cards fast. I've learnt the hard way that as Zarathur you HAVE to give up the usual focus on resources and instead block Cato's draw.
Kith, incidentally, is probably one of the warlords where I'm happy to be playing Zarathur. Its very satisfying to wipe out a bunch of Khymera at once, or to watch as the Kith player keeps trying his choke game in the face of ammo depots. DE units are low HP with decent attack values generally, and that's Zarathur's preferred target: he can dish out a load of damage before attacks even begin.
Orks can be troublesome because of their HP, but on the other hand Zarathur makes Snakebite Thugs double-punch themselves in the face, and makes their Ork Kannon weaker. His low hand size makes Smasha easier to deal with.
So in short, to beat Zarathur, bring a unit which has lots of HP, or just play Cato.