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.
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!