Is there a difference in nuance between the two? Are they interchangeable?
The only noteworthy difference between 「～～じる」 and 「～～ずる」 is that the former sounds "lighter", "less literary", "less formal", etc. than the latter.
There is no difference in meaning between the two forms. Thus, for the pure purpose of maintaining the meaning, one could say that the two are interchangeable.
IMPORTANT: Language, however, is never very simple and therefore, if you changed one word in a sentence, you might need to change some others as well to retain the level of formality, literary feel, etc. of the original sentence.
Is the latter outdated?
No, hardly not. You will encounter the 「～～ずる」 form quite often in more serious and/or formal kinds of writings/speeches.
It is just not used very often on the street, so to speak.
Lastly I've seen more of these pairs (which I don't recall at the moment). Is there a general rule to be said about these verb endings?
What does exist is more a tendency than a rule; In fact, there is no such rule. 「～～ずる」 tends to be used more often in social sciences than in natural sciences. As a Japanese-speaker, if I were asked where I would see/hear 「～～ずる」 most often, I would tend to think of proverbs, philosophical sayings, or for a lack of word, "more profound statements" in general.