I went through this question but I have context defined.
The context:
She's dear to me and I don't want to leave any stone unturned wishing her success in her exams.
The nuance as I understand it:
While 'Best of Luck' still suggests (selected answer) her making some efforts to make the best of her luck, my wish of all the best conveys the message of whatever happens, it should be the best. This should be beyond her efforts and purely luck.
Example
For instance, out of 10 chapters from the syllabus, she made great efforts and she's through with 9 of them as while getting on the tenth, she fell sick.
The result
My wish best of luck (she has to do efforts to make the best of her whatever luck) applied and the majority of the questions came from Chapter 10!
My wish all the best worked and majority of the questions came from Chapter 1-9.
Am I right? Which greeting conveys that even though your efforts don't come in use, let the luck play its role and offers you the best.
Best Answer
Interesting question!
"Best of luck" seems to say, you hope that someone will have the best luck they possibly can with a specific something (or everything in general), such that if there's any part of their experience that's left up to chance, it will go well for them, because they have "the best luck."
"All the best," which I often see as "I wish you all the best," seems to say, you hope that a specific something (or everything) will happen in the best way possible for them, regardless of how it ended up that way.
For example, wishing "all the best" means you don't know whether she'll do well because she studied hard or because the questions were ridiculously easy or because the questions happened to be about the few things she did know from the material she wasn't able to study; you just want her to do well and wish that she will.
On the other hand, wishing "best of luck" is only wishing her good luck, so only applies to situations of random chance. In this case, the questions from Ch. 10 lining up with her potentially low amount of knowledge from the chapter would be luck, and some would say that the test being easy in general would also be luck.
A potential source of confusion: "Make the best of (whatever)" is a very different phrase from "best of luck". To "make the best of x" means that regardless of how bad situation x turned out because of chance, the subject will make every effort to get a good result out of it anyway. This phrase tends to connote that x was something that did have an element of chance and that it went poorly.
So, if I heard someone say, "We'll make the best of our luck," I would assume that they ended up with circumstances that they didn't want, which are either bad or maybe simply strange, but they are determined to utilize what they do have as well as they possibly can.
Hope it helps!