I agree, "constructed" is more precise and neutral in general, and this term's usage on the ISO 639 website is another reason to prefer it.
(And, even though it's not very important, I will mention that I don't agree with the statement on that talk page: 'A more precise term for Esperanto, Ido, Interlingua, Interlingue, Lingua
Franca Nova, Novial and Interslavic is "planned language".' Language *planning* can be done with all languages, not only constructed ones. Modern Turkish, Hebrew, Mandarin, and many other languages that are definitely not constructed were influenced by language planning activities.)
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Amir Elisha Aharoni · אָמִיר אֱלִישָׁע אַהֲרוֹנִי
http://aharoni.wordpress.com“We're living in pieces,
I want to live in peace.” – T. Moore