I've used Apache exclusively for the last 3 years until just a few months ago when I set up another server to host a number of sites I wanted to move off Apache and on to Nginx. After having used both, and trying real hard here not to start a religious war as is what happens often in these kinds of discussions, I have to say neither is "better" overall or in general in my experience.
If you're familiar with Apache configuration then you should have no problem with Nginx because the way both servers structure their config files is very similar. I prefer Nginx config files however because it feels more like writing JSON whereas Apache config files are like writing XML, especially in the area of virtual hosts. That said, neither is better, its really more about what you're comfortable with and prefer. Nginx had most of the same configuration options and the tough part was figuring out what Nginx calls the corresponding Apache option.
For me there was a barely noticeable performance difference with Nginx being faster. The caveat here is that in my case I started moving all of my static sites and sites with "simple" php script type apps over to Nginx and used the apache server for a very few apps that were running more memory and CPU intensive apps. The Nginx server was also new and clean while the apache server had been in use for a great many more things including non-web applications and managing private got repos for about 20 code bases.
Nginx did use about 25% less memory in my case than apache even while serving up more sites.
I love being able to host multiple SSL sites on a single IP with no hoops to jump through with Nginx. On Apache your options are to acquire more IPs or set up SNI which for me was more hassle than it was worth.
So since we're on HN I'm assuming most people are serving Ruby or Python based apps with Nginx or using it as a reverse proxy. That's cool and all but there's still an enormous cross section of the developer community using it to serve php and as I have a lot of sites that were originally built in php my Nginx server needed Php-fastcgi. I mentioned earlier that configuring Nginx was a breeze since most of my apache knowledge transferred over but setting up fastcgi was not a breeze. It's easy to get set up and working but actually understanding what it's doing and if you really do want to configure it in the way whatever online guide shows you is the tough part. On apache you'd just install mod_php5, 'a2enmod' it, and then all you need to worry about is your php.ini file. On Nginx you have the added step of adding a config block to each server block for php. That's easy enough to get the gist of but then you start wondering if you've made the right decision after you read those warnings about improperly setting it up leading to security holes with file uploads and then you start wondering what other options should I know about, should I implement them, etc. Maybe I'm totally misguided here but with mod_php you didn't worry about security. You only worried about the security of your actual code, the server itself (firewalls, ssh, port blocking and all that), and your .ini's. So that was a downside for me but not insurmountable by any means.
It's also far easier to find information on apache than Nginx. Nginx has a ton of available support and articles and tutorials out there but most of them cover the same narrow section of topics and are contradictory sometimes. The Nginx wiki itself even has warnings about getting advice from outside the wiki in the Pitfalls section. Of course you need to be careful when sourcing information from the web no matter what the topic but I felt more secure in searching for Apache information than Nginx information.
I really love Nginx though. It can really take quite a beating without even batting an eyelash as I've seen. That said, I'll still be using Apache as my "workhorse" server for some time until I can get more Nginx experience under my belt. So I'd say take these testimonials for what they are: just testimonials. True or not, any piece of software worth using can get people to rave about it. What's important is if they're situations, expectations, and needs align with your own.