Are you a stick person or a carrot person?
That is, are you more motivated by fear or reward?
Now suppose you have a large piece of music to learn by Friday. Do you jump right to the most difficult spot and try to work that out first or do you skip the hard parts and try to learn all of the easy stuff?
The argument for the latter is usually this: as long as this is a piece you can actually play, there is usually only a limited amount of difficult material, but it can be a real morale crusher if, after several days of trying to learn a new piece, or what's worse, a deadline, you are working on the same three lines. I learned in college the fine art of skipping the second page because it was hard and discovered that by the end of the first day I actually had a grip on pages 1 and 3 through 9 (the end of the piece). That made me feel pretty good about the way things were going and allowed me to really zero in on that second page, confident that once I mastered it I would know all of it. It felt sort of irresponsible to just blip on by, but I realized that, had I tried to stick it out I might have felt pretty deflated in that I hadn't gotten very far into a long piece, and, as it turned out, the rest was not so difficult after all. Sometimes the hardest part is on page two.
On the other hand, the hard parts will take longer to learn, and thus, it is better to start them early, thus giving ourselves the most possible time between now and the performance to deal with them. Even time spent away from the piano counts because our brains never quite stop working on those problems.
I have done it both ways. Usually running through the piece to triage the materials entire is a good way to start if you've never played something before, but the choice to master quantity vs. difficultly can be made on a number of factors, such as the time you have left, the chance you can fake or skip what you have to in a worst case scenario, and what is worse: discomfort with the whole vs. discomfort with a part. In other words, fear is a great motivator.
I've been working on several Beethoven sonatas at once for an upcoming class and have saved the most difficult for fairly late in the process (after picking through it a little to give it a bit of head start with my subconscious). Since I had chosen to play around six sonatas in about a month's time I was more worried about not getting to all the music. Also, I do not absolutely have to play any particular sonata if I don't want to, but I do have to fill about 10 hours of class time.
As always, though, my mantra is to start as early as possible. That way, you can even take breaks when Beethoven is coming out of your ears and do something else for a week. Coming up for air is also an important part of the work dynamic.