It will not distinguish since both will produce Cu(OH)2.
A better test is to add BaCl2. That will ppt a while ppt of BaSO4 with the sulfate but not the nitrate.
Suppose you suspect that your unknown is either copper (II) nitrate or copper (II) sulfate. You decide to add NaOH to your known as a test reagent. Will this test distinguish between the two possibilities? If not, could you suggest a different test?
3 answers
What if I had to use barium nitrate as the test reagent, how would each one react to that?
It's the Ba ion that does the job so as long as the salt is soluble, Ba anything (BaCl2, Ba(NO3)2, etc) will work.