mRemote is well suited if you need to manage multiple types of servers and/or network devices. Instead of opening a dedicated Putty session and having to manage all of the windows, mRemote can handle all of this with different tabs. If you only have a few devices (less than 10), mRemote could be overwhelming for the need and not quite match up with what you are needing.
The primary use case is to assist an IT team working on computers across offices, or at times a server handled by another department. If it is offsite work and we need quick access. It also helps in getting access of BYOD devices of all employees and its file sharing feature is one of the most used in a few departments although support for integration with cloud service providers is a sore point.
Tabbed Views. Each server remote desktop is viewed in its own separate tab, similar to a web browser. This makes it much quicker and easier to switch between them than using separate windows.
Storing credentials. You can configure it with log on credentials for each system, saving time on accessing as you don't need to enter a password each time.
Multiple connection types. I use the traditional RDP the most, but mRemoteNG allows many different connection types, similar to Putty.
It's very easy to setup and use. The tree structure organizes the multiple connections in a hierarchical manner which makes it easy to browse and the tabbed browsing make it simple to switch between multiple ongoing connections You can even export the list of connections and import it to another setup.
mRemoteNG is far more useful than LogMeIn when on the same network, or VPN as the servers, as it allows multiple server screens open in multiple tabs. LogMeIn is much more useful when working out of the office for its ability to connect anywhere, but each system accessed is in a separate window making navigation a little tricky. Sometimes I use them in tandem however, LogMeIn to access a machine in my network, then mRemoteNG to access multiple machines from there!
From a strictly remote access perspective, the experience is virtually the same between the big three remote access solutions - ShowMyPc - LogMeIn - TeamViewer. They all offer similar connection experiences. ShowMyPC has the best browser based experience - very smooth and seamless. LogMeIn's is lacking and the experience feels sluggish. TeamViewer does not offer this to my knowledge. ShowMyPC wins with the free on-demand access because it is handled via the browser. [TeamViewer] offers free - but only via a downloaded client. LogMeIn does not offer anything for free here.