Nagios or Icinga
Is an open-source computer system and network surveillance application. It keeps an eye out of servers and services, that you specify and sends messages when things break down, and when services or servers are back on-line because of a temporary hick-up.
here are some pro's why you might wanna use Nagios:
- Is a industry standard
- Exist for roughly 14 years. Is a bit more mature
- Popular then Icinga according to Google search requests
- Nagios training is wide available
The original developer is the main developer and gatekeeper. meaning the 'core'-nagios is written by one person, and certain features that would have to be approved by him. Although this is not longer the case  . Even after the main developer allowed other developers to work on nagios-core', the speed in terms of bug fixes, are not optimal, compared with that of Icinga. It is also not feature rich nor fast with its feature integration , - such as PostgreSQL and Oracle database support - here Icinga wins.
Feature integration, and bug fixes, hangs on whether the developers acknowledged it as a bug, and also wants to fix it. Feature integration is also a developer's choice. is it a feature that could actually benefit the main applications, and that is actually gonna be used.
Icinga is a open-source network and computer system monitoring application. is was originally developed as a fork of the Nagios system monitoring application in 2009.
Here are some pros for Icinga:
- completely open-source
- Allot of Nagios plug-ins also work with Icinga(And vice-versa)
- Feature integration is much smoother
- Bug fixes faster(although this depends on the company, if they actually see it as a bug, and or a highly needed feature)
- Although there are allot of Nagios plug-ins that work with Icinga not all of them will
- is a bit younger project compared to Icinga(~4 years)
- training is not widely available compared to Nagios
Why a fork?
Because only one person wrote the Nagios core code. And he did not want more people to work on it. The community made several bold attempts to change this. This lead to Nagios asking long-acting community projects, say they were not involved with Nagios. And in some cases they were asked to change their open-source project name. And also if they wanted to transfer there domains. 
To overcome the above obstacles long time community developers decided to fork Nagios, and above all, to further the development of this popular monitoring software
Why Icinga in stead of Nagios? Nagios developer(Ethan Galstad) was more busy whit his own company – selling of nagios training – and not on actually working on Nagios. Feature and bug-fixes did not get the attention that Ethan Galstad could give, or wanted to give. The Icinga community is more lively in that.