In short, it depends on why the test is being used.
Diagnostic tests can be used to measure how much a test-taker already knows about a specific content area, and to identify areas which may need further improvement.
These tests can be used specifically on known areas of difficulty, and often the total score on these tests are less important than being able to identify which questions in the test were difficult, and whether there are commonalities in incorrect questions.
There is a lot of attention given to minute details, often with no time limit, no norms and extensive feedback to the test-taker.
Achievement tests can be used for comparison purposes, i.e. to assess the performance of a test-taker against a group of test-takers, and to rank test-takers according to performance. These tests can often include a wide content area, a range of question difficulties, a fixed time limit and a focus on the total score. These tests generally include norms.
A lot of people use achievement tests for purposes such as identifying how well a teacher teaches, how much a student has learned or to assess the quality of a curriculum, but this is not appropriate since these tests can often include skills or information that students were not taught.
So whether you are trying to determine what a test-taker has already learned and what their performance is for specific knowledge area OR what the source of a specific learning difficulty is for the test-taker, you need to be aware that it is important to implement the appropriate type of test.