I found that there was a difference in the amount of words per unit (hence you wrote slightly longer assignments for any course work units).
There was also a greater expectation regarding research literature (number of references and the quality of your references used within assignments and with research tasks). You were expected to take a more rigorous critical stance with what you read and had to complete obligatory research methods units as well.
There were also more expectations with regard to the level of critical engagement with your arguments and approaches. However,
while the expectations were higher, most people doing well in their final year of undergrad studies are well able to step it up and it doesn't always feel like a huge leap-more just what feels appropriate at the time (if this makes sense).
When it came to the minor thesis (or dissertation or whatever your university and system call this aspect of the MA), however, I did find that there was a noticeable difference. My minor thesis was around 25 000 words and it was a good preparation for the PhD. I found aspects of this pretty challenging at times-as noted-good preparation for further research. (Sorry I should qualify also-I've just realised that you mentioned doing an MA- I did an MEd with the minor thesis as the specialty so info may differ for MAs. If so pls just ignore).