Does Hammer of the Righteous cause more threat than Crusader Strike?

I don't know that "more threat" is the right phrase to use. Because of the mechanic changes with the patch, Crusader Strike and Hammer of the Righteous are for two different situations. Hammer of the Righteous has no use in single target fights. You should only be using it on multiple target fights. For single target fights, you'll use Crusader Strike as your primary threat builder.

The technical answer to your question is that Crusader Strike provides more threat per target than Hammer of the Righteous, but when you are tanking multiple mobs, Hammer of Righteous provides more threat spread across the enemies.

Hammer of the Righteous has been nerfed to deal significantly less damage from a single target point of view, but have an AoE attack.

However, it is worth noting that:

• Both are on the same cooldown length, 4.5 seconds.
• Both share cooldowns, so that using one places them both on cooldown.
• Crusader Strike is meant to be used in a single target rotation.
• Hammer of the Righteous is meant to be used in a multiple target rotation.