Allow me to clarify. When I say more detail I mean things like type are sharper. When I say more things I mean things you don't see otherwise.
So because both browsers scale up to fit the width:
In portrait the Nexus has a taller screen. Both screens show the same amount of the website widthwise but you see more things vertically. You don't have to scroll as much to see the same content.
In landscape the Nexus screen is wider but shorter. So both screens show the same amount of things widthwise, but the Nexus shows fewer things vertically.
The Nexus still has more resolution in landscape than the mini - its resolution - 1280x800 - is greater in both orientations than the Mini's 1024x768. You will see more in width and height on the Nexus, regardless of how you hold it.
Even though the screen is physically narrower on the Nexus, you'll still have 32 more pixels of 'stuff' on your screen.