"Just" versus "simply"

To which extent is just interchangeable with simply, as in the example?

It's becoming more than just annoying.
It's becoming more than simply annoying.

Is just synonym of simply in just any case or are there situations where the two adverbs convey slightly different meanings?

Also, Google gives 1,800,000,000 results for just and only 295,000,000 results for simply. Is one preferred over the other?

Just and simply have some overlapping meanings, but definitely do not overlap in all meanings. In your example, it is a case where they have essentially the same meaning.

However, just (the adverb) can also mean "only now". For example:

How long have you been here? — I just got here. (=I arrived right now.)

Simply cannot be used in this instance.

(Note: I assume that we are only talking about just as an adverb; just can be used as an adjective too, meaning "right" or "fair". I don't think you are concerned about that one, because it is clearly totally different in usage.)

The second sentence sounds odd and is incorrect. "Just" and "Simply" do not have the same meaning, however, these can be interchanged in most situations; though not in this one.