Well, yes and no. depending upon how one defines "compatibility". For example, let's say a Windows user sends you an Office Word document that you want to open in Pages. Whether it is 100% compatible is dependent upon what the Office user included in the Word document, your own fonts, printer drivers, and so on.
For example, this table of Word to Pages shows features that are supported, partially supported, and not supported.
Pages - Mac Compatibility - Apple
While the bulk of the features are clearly common to both operating systems, it is the partially supported or unsupported features that can drive users of either OS up the proverbial wall. For example, bulleted lists, some paragraph styles, partial carry over of headers or footers.
Here are the other charts for Numbers and Keynote
Numbers - Mac Compatibility - Apple
Keynote - Mac Compatibility - Apple
Here is quote from Jim Gordon, an MVP participant on MS Forums, a little dated and it refers to older versions of Word, but it has important caveats. The key line is at the end "Inevitably, some documents may need to be tweaked, as a result."
Windows to Mac Compatibility - Microsoft Community
As for having documents be identical when moving from one computer to another there are factors you must consider. This is true PC to PC, PC to Mac, Mac to Mac, and Mac to PC. Microsoft Word is a word processor that has text that flows, unlike a PDF or page layout program. Any difference in font or printer driver from one machine to another has the potential to affect spacing, breaks, window & orphans, paragraphs, etc. To repeat - these changes have nothing to do with Mac to PC, rather they are caused by computer to computer differences.
Your documents should look the same on the Mac as long as ALL of these conditions are met:
* The documents on the PC originated in Microsoft Word 2010 with service pack 2
* The documents were saved in a current OOXML file format in Word 2010
* The documents used only fonts supplied with Microsoft Office 2010
* Old versions of the same fonts are not installed or active on either the Mac or the PC
* The documents are opened on the Mac in Microsoft Word 2011
* The current versions of the Microsoft Office fonts are active on the Mac
* The printer driver on the Mac behaves identically to the printer driver that was being used on the PC where the documents were saved.
The behavior of Word is identical on the two platforms with regard to the formatting you expressed concern about. There are conditions that must be met if you want your documents to look alike when moving from one computer to another - regardless of platform. It's the fonts, file formats and printer drivers that are the sticky points when moving a document from one computer to another regardless of platform.
These are hard to control from a user perspective. In Word 2010 with SP 2 you could use macros to make sure your documents have only Microsoft Office fonts and are saved in the current file format before bringing them to the Mac, and even save them as a PDF for future reference. You won't have control over how exactly matching your printer drivers will be - even if you are using the same printer. Inevitably, some documents may need to be tweaked, as a result.
And I would also say that his words apply as well to Windows users who are exchanging Office documents among themselves created in different versions. "Inevitably, some documents may need to be tweaked, as a result."