From what I've seen on the market, Nginx and Cherokee are pretty interchangeable for what you're doing. If you've already got things set up on Nginx ... there's no reason to switch to a different system.
But if you want some benchmarks ... I did a quick Google search and came up with these:
In the end, it all depends on what you care about the most. If you're running WordPress with caching enabled, you'll be more concerned with static content. If you're running a multisite installation without caching (something I do), you'll likely be more concerned with dynamic content and stability/security.
From a general usability standpoint, though, it's safe to look at the market leaders and use them as a canary-in-a-coal-mine.
WordPress.org recommends Apache for a server because it's easy to set up and comes pre-configured on most hosts. However, Automattic elected to use Nginx to host WordPress.com. They have their own reasons ... but I elected to do the same for performance reasons (and so I can run some asynchronous servers using the same system via Node.JS).