There is no easy way (with a shortcut) like in LR. The only way I was able to achieve this was via workspaces. It's a pain (since you can't easily make a shortcut for workspaces). Also, to make it a little bit easier, add the workspace icon to your toolbar for each of the new workspace. This way you don't have to go through the menu each time you want to change.
Assuming you're on a Mac you can make a shortcut for workspaces using the standard OSX system preferences > keyboard > keyboard shortcuts by simply referring to the name of the workspace. This takes less than 60 seconds, and you only have to do it once :-).
Or you can add a standard C1 keyboard shortcut (using Capture One > Edit Keyboard Shortcuts) for "hide viewer" so that you can use one hand and two quick shortcuts (only slightly
more work than one shortcut) to hide/show the browser and hide/show the viewer.
But IMO it's best not to try to make one program emulate the behavior of another, but rather embrace the advantages and disadvantages of each program to make each work to it's best ability. For instance if you are at a stationary system I love two monitor setups and C1's ability to provide browser, tools, and a 100% preview on one monitor, and the full-screen of just the image and histogram on the other monitor. Whatever your goals/workflow needs there are likely several layouts C1 can provide you that would be more efficient than simply trying to emulate what you had previously done in a separate software suite.
We cover a lot on layouts for efficient workflow in our Capture One Training