Which LMS do you use and why?

You should not base your choice just on opinions of others. You are most likely trying to identify software that will be used in your company over next couple years. Consider performing a proper evaluation to make the right choice.

We approached this by creating a matrix of desired functionalities we would expect from out LMS of choice, i.e. requirements in terms of customizability, user management, compatibility with our existing content, etc. Next steps were to give weights to these various requirements and score a number of promising LMSes on the market.

One of the key factors I would consider is an Open Source. Although some of the closed-source commercial products still offer a lot of additional functionalities not present in OS, you gain flexibility to tailor the system to your specific needs. You also have a chance to expand it without waiting for mercy from a commercial vendor.

After thorough comparison we have chosen to go with ILIAS. It has won mostly for following the standards (no or easy to troubleshoot problems with SCORM), decent functionality and very good clean, object oriented code. Also unlike Moodle, it is a very controlled project with clear division of responsibility between the parties involved in its development.