Nginx vs Apache

http://www.itworld.com/article/2695421/choosing-a-linux-web-server-nginx-vs-apache.html
Nginx has become popular due to its event driven design which can make better use of today’s computer hardware that Apache’s process driven design. The end result is that nginx can serve more concurrent clients with higher throughput than Apache on the same hardware. 

If you’re going to be serving a single site and this server is dedicated as a web server with a separate database server, you will likely be able to find some gains by using nginx over Apache if you have high traffic. As an additional benefit, nginx has configuration features which make it easier to scale than Apache if necessary.
https://www.wikivs.com/wiki/Apache_vs_nginx

Apache is a flexible server which can be process-based, thread-based or event-based as determined by the MPM used, while nginx is an event-based web server.

Nginx and Lighttpd are probably the two best-known asynchronous servers and Apache is undoubtedly the best known originally process-based server. [...] The main advantage of the asynchronous approach is scalability. In a process-based server, each simultaneous connection requires a thread which incurs significant overhead. An asynchronous server, on the other hand, is event-driven and handles requests in a single (or at least, very few) threads.

https://www.digitalocean.com/community/tutorials/apache-vs-nginx-practical-considerations
Apache is often chosen by administrators for its flexibility, power, and widespread support. It is extensible through a dynamically loadable module system and can process a large number of interpreted languages without connecting out to separate software.
Because of this popularity, Apache benefits from great documentation and integrated support from other software projects.

Nginx has grown in popularity since its release due to its light-weight resource utilization and its ability to scale easily on minimal hardware. Nginx excels at serving static content quickly and is designed to pass dynamic requests off to other software that is better suited for those purposes.

Nginx is often selected by administrators for its resource efficiency and responsiveness under load. Advocates welcome Nginx's focus on core web server and proxy features.

Connection Handling Architecture

One big difference between Apache and Nginx is the actual way that they handle connections and traffic. This provides perhaps the most significant difference in the way that they respond to different traffic conditions.

Apache

Apache provides a variety of multi-processing modules (Apache calls these MPMs) that dictate how client requests are handled. Basically, this allows administrators to swap out its connection handling architecture easily. These are:

• mpm_prefork: This processing module spawns processes with a single thread each to handle request. Each child can handle a single connection at a time. As long as the number of requests is fewer than the number of processes, this MPM is very fast. However, performance degrades quickly after the requests surpass the number of processes, so this is not a good choice in many scenarios. Each process has a significant impact on RAM consumption, so this MPM is difficult to scale effectively. This may still be a good choice though if used in conjunction with other components that are not built with threads in mind. For instance, PHP is not thread-safe, so this MPM is recommended as the only safe way of working with mod_php, the Apache module for processing these files.
• mpm_worker: This module spawns processes that can each manage multiple threads. Each of these threads can handle a single connection. Threads are much more efficient than processes, which means that this MPM scales better than the prefork MPM. Since there are more threads than processes, this also means that new connections can immediately take a free thread instead of having to wait for a free process.
• mpm_event: This module is similar to the worker module in most situations, but is optimized to handle keep-alive connections. When using the worker MPM, a connection will hold a thread regardless of whether a request is actively being made for as long as the connection is kept alive. The event MPM handles keep alive connections by setting aside dedicated threads for handling keep alive connections and passing active requests off to other threads. This keeps the module from getting bogged down by keep-alive requests, allowing for faster execution. This was marked stable with the release of Apache 2.4.

As you can see, Apache provides a flexible architecture for choosing different connection and request handling algorithms.

Nginx

Nginx was designed from the ground up to use an asynchronous, non-blocking, event-driven connection handling algorithm.

Nginx spawns worker processes, each of which can handle thousands of connections. The worker processes accomplish this by implementing a fast looping mechanism that continuously checks for and processes events. Decoupling actual work from connections allows each worker to concern itself with a connection only when a new event has been triggered.

Each of the connections handled by the worker are placed within the event loop where they exist with other connections. Within the loop, events are processed asynchronously, allowing work to be handled in a non-blocking manner. When the connection closes, it is removed from the loop.

This style of connection processing allows Nginx to scale incredibly far with limited resources. Since the server is single-threaded and processes are not spawned to handle each new connection, the memory and CPU usage tends to stay relatively consistent, even at times of heavy load.

Static vs Dynamic Content
ginx does not have any ability to process dynamic content natively. To handle PHP and other requests for dynamic content, Nginx must pass to an external processor for execution and wait for the rendered content to be sent back. The results can then be relayed to the client.

File vs URI-Based Interpretation
In Nginx, modules are not dynamically loadable, so they must be selected and compiled into the core software.
https://anturis.com/blog/nginx-vs-apache/
One popular configuration, for instance, is to use Apache to server up static web pages and the mod_jk module to run Java and JSP code on Tomcat to make an interactive application. Another example is using mod_php to execute php scripts without having to use cgi.
Apache

Worker mode uses less memory than forked-mode, because processes consume more memory than threads, which are nothing more than code running inside a process.

Moreover, worker mode is not thread safe. That means if you use non thread-safe modules like mod_php, to serve up php pages, you need to use pre-forked mode, thus consuming more memory. 

Nginx

Nginx does not create new processes for each web request, instead the administrator configures how many worker processes to create for the main Nginx process. (One rule of thumb is to have one worker process for each CPU.) Each of these processes is single-threaded. Each worker can handle thousands of concurrent connections. It does this asynchronously with one thread, rather than using multi-threaded programming.

The Nginx also spins off cache loader and cache manager processes to read data from disk and load it into the cache and expire it from the cache when directed.

So if your website is predominately Python or Ruby, Apache might be preferred for your application, as Apache does not have to use CGI. For PHP, it does not matter as Nginx supports PHP internally.

http://tutorials.jenkov.com/nginx/index.html