There are mostly aesthetic and workflow streamlining changes.
The Office logos have been updated, and the tabs have been renamed. Recent documents are shown in a list rather than tiles. OneNote is a separate app and is not in the Office Hub. The recent documents list is synchronized with Office 2013 and Office Online.
In the individual apps, the top bar is a solid color (e.g., blue for Word) rather than white/transparent.
Word is basically identical in WP7.5 and WP8.
The column and row headings are prettier. The Outline button has been changed to Sheets. You can sort numbers with the new Sort button. Comment has been moved from the action bar to the overflow, and Sort has moved from the overflow to the action bar.
Selecting text to edit is more direct. In WP8, you directly tap on the text, whereas in WP7.5, you tap the slide and press the Next button to go through the different text boxes. Notes are below the slide, no longer accessed through the Notes button. Outline has been changed to Slides .
You can use Speech or Cortana to add notes. Navigation is different because OneNote isn't part of the Office Hub.