As an American, I tend to use "no problem" when the value of what I gave was much less than the utility they got out of it, such as when I already know the answer to a problem they've spent a lot of time researching -- for me, it's 30 seconds of recalling information, while for them, it's 30 minutes of time saved. So the person I helped ends up much more thankful than I am put out, and deflecting the need for any thanks is appropriate in my eyes.

I tend to use "you're welcome" when it's things like getting called at 4am to come pick up a friend whose car broke down in the middle of nowhere. There's absolutely no way there their request didn't mess up my day, just due to the timing and time commitment involved, so it seems more appropriate to take their thanks seriously.

But on the whole, I think both are accepted well enough by native Americans in both situations, and it's one of the less important details of the language to worry about.

I'm confused because, etymologically, there's no difference between the two statements. I see them as two parts of a whole, in fact: "it was no problem; you're welcome to ask again." An "any time" can also show up in there.

Except that for some favors, it's not true that "It was not problem", even if it is true that "you're welcome to ask again". In these cases, I use "you're welcome".

In the others, I use "no problem".