As noted in the Troubleshooting section of the Munki wiki, you can increase the logging level for Munki clients.

The default logging level is 1, which looks like this:
Dec 12 2019 20:04:20 -0800 GoogleChrome version 79.0.3945.79 (or newer) is already installed.

If you increase the logging level to 4, it will look like this:
Dec 12 2019 20:08:23 -0800 DEBUG1: Found GoogleChrome, version 79.0.3945.79 in catalog testing
Dec 12 2019 20:08:23 -0800 DEBUG1: Found Info.plist at /Applications/Google Chrome.app/Contents/Info.plist
Dec 12 2019 20:08:23 -0800 DEBUG1: Checking /Applications/Google Chrome.app/Contents/Info.plist for CFBundleShortVersionString 79.0.3945.79...
Dec 12 2019 20:08:23 -0800 DEBUG1: Using version_comparison_key CFBundleShortVersionString
Dec 12 2019 20:08:23 -0800 DEBUG1: Installed item has version 79.0.3945.79
Dec 12 2019 20:08:23 -0800 DEBUG1: Installed item is the same.
Dec 12 2019 20:08:23 -0800 DEBUG1: Found Info.plist at /Applications/Google Chrome.app/Contents/Info.plist
Dec 12 2019 20:08:23 -0800 DEBUG1: Checking /Applications/Google Chrome.app/Contents/Info.plist for CFBundleShortVersionString 79.0.3945.79...
Dec 12 2019 20:08:23 -0800 DEBUG1: Using version_comparison_key CFBundleShortVersionString
Dec 12 2019 20:08:23 -0800 DEBUG1: Installed item has version 79.0.3945.79
Dec 12 2019 20:08:23 -0800 DEBUG1: Installed item is the same.

which looks very similar to the output from a manual sudo managedsoftwareupdate -vvv run:

Found GoogleChrome, version 79.0.3945.79 in catalog testing
Found Info.plist at /Applications/Google Chrome.app/Contents/Info.plist
Checking /Applications/Google Chrome.app/Contents/Info.plist for CFBundleShortVersionString 79.0.3945.79...
Using version_comparison_key CFBundleShortVersionString
Installed item has version 79.0.3945.79
Installed item is the same.
Found Info.plist at /Applications/Google Chrome.app/Contents/Info.plist
Checking /Applications/Google Chrome.app/Contents/Info.plist for CFBundleShortVersionString 79.0.3945.79...
Using version_comparison_key CFBundleShortVersionString
Installed item has version 79.0.3945.79
Installed item is the same.

So if you want to see the equivalent of managedsoftwareupdate -vvv in the /Library/Managed Installs/Logs/ManagedSoftwareUpdate.log, I’d recommend using LoggingLevel 4.