LAMP is an acronym for a model of web service solution stacks, comprising of these components: Linux (can be Ubuntu, CentOS, etc), Apache web (HTTP) server, MySQL database and PHP programming language. This is a combination of components which is very popular and has been around for quite some time.
LEMP is pretty much similar stack of components as LAMP, except the Apache is being replaced by nginx. Pronounced "engine-x", which explain the E on "LEMP", nginx is a HTTP proxy application with reputably much smaller footprints compared to Apache, allowing it to handle higher load of HTTP requests. Nginx uses an asynchronous event driven approach to handling requests, compared to Apache's default threaded or process oriented approach, and its modular event driven architecture can provide more predictable performance under high loads.
Let me try to summarise in points on the advantage and disadvantage of using Apache and nginx.
Apache:
Nginx:
To conclude, nginx is faster and able to handle much higher load compared to Apache using the same set of hardware. However, Apache is still much better in terms of functionality and the availability of modules required to work with back-end application servers and to run scripting languages. So, it really depends on what you want to run on your web server.
It is actually possible to run both Apache and nginx on the same server, so you can have the best of both worlds. For example, you can run nginx as reverse proxy while Apache is running in the back-end.