I have not run any Yii-developed applications under heavy load with Nginx/PHP-FPM yet.
I have, however, been running a production server for the past year, configured with Nginx + PHP-FPM for an LMS (Learning Management System) called Moodle.
Moodle is very heavy, poorly developed, poorly optimized. We had initially set it up to run under Zend Community Server (Apache + PHP module with some tweaks from Zend), which performed poorly, had unusual issues, etc.
Switched the server to Nginx+PHP-FPM, and the Moodle site has run smoothly ever since, with maybe 2 hiccups in roughly 260 days of server uptime (the hiccups were unrelated to nginx/php).
Considering how light Yii applications are, combining with Nginx & PHP-FPM should be the perfect mix.
Once I have Yii applications that are experiencing moderate to high loads, I’ll be able to better determine how well it performs with Nginx.
I highly recommend Nginx over Apache, as I’ve been using Nginx for a couple of years now, and my experience has only gotten better and better, whereas with Apache, my experience only ever got worse.
As you’re considering switching, I highly recommend testing a small cloud instance so you can get familiar with configuring Nginx & PHP-FPM.
Both are quite different from what you may have experienced with Apache.
I tend to use Rackspace Cloud Servers for inexpensive instances, as I can have a decent server that functions surprisingly well for ~$22/mo
I also highly recommend using Ubuntu/Debian for web server deployments, as it’s more up-to-date on software than Redhat-based distros, which is important when you’re talking about something like Nginx that has had important features added across each release.
I’ve heard good things about Linode as well, haven’t used them myself though.
Rackspace has worked well for me, so I use that for personal testing/hosting due to low cost.
For my employer, we use StormOnDemand.com, which has worked well, but the cheapest cloud server is $50/mo I believe (though they may have a new lower tier now). Rackspace is still likely better bang-for-the-buck regardless, as you get a "quad-core" instance from Rackspace in their cheap plans, whereas Storm is a "single-core" instance I believe.
Whatever you do though, avoid SoftLayer Cloud like the plague. Horrible horrible service. Their dedicated servers are fine, if a bit pricey for what I would personally pay.
I know alot of people are fond of Amazon Cloud, but I keep seeing/hearing people get high bills because they under-anticipate how much Amazon actually costs. Typically not a cheap service unless you fire up an instance for just a few hours.