It depends on what you are trying to import from and a few other factors.
Check out the Help in Monarch and search for the 'Settings' information.
In my experience the workfile table will stop growing and importing at about 1Gb or a little over. However this relates to what you are doing within the import, calculated fields and so on, not just the size of the file being imported. (Or more specifically the size of the components of the file being imported.)
I'm not sure that you can make a useful comparison between Access and Monarch since the purposes are different I think. If you have a file that can be imported directly to access with no changes or additions than it makes sense to import it directly. Otherwise Monarch is probably a more usable and flexible tool unless you are an Access expert and a Monarch novice.
The internal engine that Monarch uses to create it's tables is based on Microsoft's Jet Technology. That being said, these are the limitations to ver 8: