When comparing PuTTY vs MobaXterm, the Slant community recommends PuTTY for most people. In the question“What are the best SSH clients for Windows?” PuTTY is ranked 4th while MobaXterm is ranked 7th.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Free
Pro De facto standard client for SSH, Telnet and Rlogin on Windows
PuTTY is one of the oldest and most popular clients. It has earned the trust of a great number of users over a long period by being reliable, offering useful features and helpful support. It got into the 15 Essential Open Source Tools for Windows Admins list by InfoWorld.
Pro Can be used on any Windows computer, even without admin rights
Pro Source code available
Full source available. Compile and modify it yourself.
Pro Lightweight and portable
Doesn't require much resources (memory and hard-disk). Can even be run on a system by just downloading without install.
Pro Flexible
MobaXterm can connect to practically anything.
Pro X server support
In case you need X11 forwarding, MobaXterm has an integrated X server.

Pro Full linux subsystem with package manager
And you can install conda for additional package management.
Pro Tabbed or split mode
Multiple terminals can either be in tabs or split horizontally or vertically.

Pro Integral remote file editor
Edit remote files via ssh and sftp
Pro SSH tunnel controls and forwarding UI controls makes it easy
Pro Automatic SFTP
With MobaXterm, there's no fiddling with multiple apps: simply connect and everything is available.
Pro Connection manager
Pro ENV can use Windows PATH
Pro Password vault
Pro Server tools (HTTPD, SSHD, SFTPD, TTFT)

Pro Build in sftp file manager
Manipulate and edit remote files in the file browser.

Pro Integrates with WSL
Integrates perfectly with the Windows Subsystem for Linux. Out of the box it offers a shell to that system.
Pro Supports macro controls (multi commands in single screen)
Cons
Con Only one session per window
Cannot open a second session in the same window (you need multiple windows).
Con Can not save passwords
Anyway, you can use "PuTTYgen" to generate a key pair, then use "Pageant" to do a password-less SSH remote login.
Con Lacks features
It is JUST an SSH client. There are many other options with built in X-servers, Multitabbing, etc.
Con Ugly design, too simple
Looks very dated. Does the basic functions very well, but not much more.
Con No global settings
If you want to change a setting for all your connections, you'd have to do it individually.
Con Organizing sessions
Does not have features for organizing session connections (like folders). If you have 5-10 connections that's fine. But if there are 30-50 connections - that becomes a nightmare.
Con Tedious logging/tracing
Its tedious to set up logging and tracing (e.g. for serial connections).
Con No login scripting
Con Not completely freeware
If you use MobaXterm at work, they hope you will pay for it. This isn't horrifying, but it's not providing any new features in Linux to warrant the outlay. Its integration with Putty in Windows as an X client may make it worth the funds.
Con Split screen prevents tabbed mode
If you split a screen within a tab, you have to go back to single screen before you can switch to another tab.
Con Can have some performance issues
MobaXterm can have some occasional performance issues. These happen rarely but it's worth mentioning that they exist, especially since this is a paid tool.
