Let's talk about the differences between a few terms first.
Updates vs. Upgrades:
You mention "the latest version," of the software, so I am guessing you mean the latest major release of the software right (i.e. version 1 to version 2)? In that case, you want to refer to an "upgrade" not an "update."
Check out this explanation on the English Stack Exchange: Difference between an Upgrade and an Update
In short, the way I have always understood it:
Updates - these apply to the current version of the software (just like patches)
Upgrade - this is basically a new and improved piece of software (a new version)
Note based on your comment above:
An update can provide new features as well (but they apply to the current version of the software). Those same features may also be included in new versions of the software but just as features (not updates).
Patches vs. Updates:
Check out this question. Someone says "all patches are updates, but not all updates are patches". You can have an update to a version of software that is not necessarily fixing a problem (what a patch would do). It may be adding a new feature. However, a patch is considered a type of update.
Back to the Question: To Upgrade or To Patch and Upgrade?
According to Wikipedia:
A patch is a piece of software designed to update a computer program
or its supporting data, to fix or improve it.
A patch is generally used to fix the current version of the software. This may be oversimplifying it a bit, but if you upgrade, it's like you're getting an all new piece of software. So, even if both A and B have different versions, if there is a new version out, there is no need to patch and then get the new version. When you get a new version, it's like your starting fresh. You no longer remember the old patched up version of the old software.
Also, just from personal experience, let's say A and B both work at a particular company, that company may require both of them to upgrade to the newest version when it is available.
Hope that helps!