"Pretension" and "pretentiousness" are synonyms only when "pretension" is used in the sense of "5b. The unwarranted assumption of dignity, merit, etc.; the use of affectation to impress; pretentiousness, ostentation; an instance of this, " as in
1904 H. James Golden Bowl I. i. 24 He also took himself seriously—made a point of it; but it wasn't simply a question of fancy and pretension. (OED)
The Longman Dictionary of English Language and Culture (2005) adds that in this meaning the word "pretension" is formal and uncountable:
pretension: 2. [U] fml pretentiousness
In modern English, the word "pretension" is usually used in the sense of "5a. A claim or profession to be or have something, as a quality, skill, etc.". In this meaning, it is almost always plural - pretentions to something or to do(ing) something. Here, "pretension" and "pretentiousness" are not synonyms.
The authors of the MW Dictionary of Synonyms add that "pretension" is "rarely used as a concrete act, appearance, or statement" [emphasis mine - Alex B.].
Also compare the following examples:
She has a pretentious accent. => the pretentiousness of her accent [pretention is not possible here]
This song has such pretentious lyrics. => the pretentiousness of the song lyrics [?pretention is questionable here]