Apache is not a synchronous web server. Apache has a mode of operation that is synchronous. It also has an asynchronous mode. In it's asynchronous mode, it is just as fast as nginx, yet supports many more 3rd party modules.
Apache 2.2 ships, by default, in synchronous mode. Why? Because Apache is commonly used to make a LAMP stack. PHP in the form of mod_php historically does not play well in a threaded environment, usually due to it's extensions.
The solution is to run php-fcgi instead of mod_php when running asynchronously. This is actually better since it separates the PHP interpreter from the request handler, which increases performance. This model, php-fcgi and asynchronous workers, is exactly how nginx works, and the two are comparable in speed in this configuration.
So why isn't this the default configuration for Apache/PHP? Ease of upgrade. It is too confusing, say packagers, to ask people to change how they deploy their PHP apps on Apache, it cannot be changed. Also, the package will include almost every stock Apache module, and they will all be loaded by default.
So install LAMP on Ubuntu, and you get the slowest possible way of serving PHP, by design. Install nginx, and you get the fastest. This is where the lighty/nginx/New Cool argument comes from, people install the stock configuration and think Apache is some slow beast that takes all your RAM.
Apache, properly configured, is amazingly fast and light on memory. Plus, you get the entire ecosystem of Apache modules to use. There are many books written on Apache module development, and thousands of books on Apache configuration and howtos.
Finally, about web servers. Web servers are an amazingly popular bit of software to write. It's so simple to do, that they massively proliferate, each claiming to be the fastest most agile web server going - I'm looking at gunicorn, Tornado, et al here.
I'm not going to comment on their speed, but instead the speed of the thing you are serving. Frankly, how fast the web server does it's web server tasks is massively irrelevant in the overall scheme of things. Any request involving DB queries will swamp the amount of time the web server spends handling the request. Any request not involving DB queries is a static file, and should be served from cache or disk, which is a hard thing to do slowly.
There is nothing wrong with nginx or lighty, they are both excellent web servers. But so is Apache, and rumours of it's death are greatly exaggerated. If you already have Apache skills, changing to nginx means learning new syntax and gotchas, and losing all your experiences and custom modules, and it still won't go faster than your app.
tl;dr - use Apache 2.4, event MPM and php-fcgi.