What's the difference between the .MSI and .EXE Toad for Data Analysts Base installers?
The two files are basically the same product.
The .MSI is typically used for companies who want to push out the product silently or re-package it in some other way.
The .exe is the same .msi but it also contains checks for pre-requisites. (e.g. The .exe will check for the presence of Microsoft .NET Framework 3.5 SP1.)
The current Release Notes and Install Guides can be viewed here.