tikz. The advantage of
tikz over graphical methods are analogous to the reasons to use LaTeX in other situations:
To write documents, many people in science use LaTeX instead of word-processing software. It has a steep learning curve, but saves time in the end and produces better-looking results.
To create presentations, quite a number of people use beamer instead of powerpoint-like software. Probably a bit less than #1, but the story is the same: It has a steep learning curve, but saves time and produces better-looking results in the end.
Some people use
pgfplots) to create their graphics. Probably a considerable lower number than in #1 and #2, but again, the reasoning is the same: It has a steep learning curve, but...
Does it start to sound familiar? I guess it should! For a long time, I used LaTeX only for #1. When I prepared my Master thesis presentation, I made the jump and decided to learn beamer, and then I used LaTeX for #1 and #2. Then, when I was writing my licentiate thesis (midterm PhD thesis in the Swedish academic system), I wasn't satisfied with the diagrams and plots, and decided to learn
pgfplots. So then I used LaTeX for #1, #2 and #3.
That's my current situation. I don't know right now if I will make any further steps in the forseeable future. If any, it would be package writing, but so far the prospect of programming in TeX looks daunting to me. Quite possibly the reasoning will once again be the same: It has a steep learning curve, but...
P.S. Of course, you can always use other programs to create graphics and then draw on top of your picture!