Different academic institutions may follow different policies to deal with this issue. It may also depend upon the teachers how favorable they are for their students. Some might be soft hearted while others may be stuck to the policies.
If we compare being late with being incomplete, I would say being incomplete is still a better option. When you submit your assignment late, teachers may deduct your marks up to 50% or even more. While on the other hand, a timely submission with few incomplete sections may still help you save some marks.
But the best option is that you should always complete your work in time and submit before the deadline is over. And the best way to stay away from trouble is to seek the help assignment if you are stuck somewhere in middle of the process.