The PHQ-9 has the advantage of being faster to apply because it has fewer items, but the BDI-II is more complete and, therefore, more reliable in addition to having more literature on it: in short, I advise -if you can choose between the two, the BDI-II.
I believed that, according to the literal text of the Question, it inquires about two specific Questionnaires or Inventories and that they evaluate Depression ... but, in view of other answers, it is clear that I misunderstood the question; So, if we can talk about other Tests that measure more things than Depression, the most complete and, therefore, advisable are the "MMPI-2" or the "MMPI -2-RF" and the Test of the 90s. symptoms ("The Symptom Checklist-90-R" or "SCL-90-R")
I think it depends what you want it for. The PHQ-9 is brief and reliable, and has a clinically important difference metric to assess change over time, but people often use the 8-tem version (no CID yet I don't think) as it omits the final question about suicide.
The HADS is also an excellent scale to use for those with physical health complaints because the items do not include somatic symptoms that can often be due to physical health (such as fatigue/insomnia, GI problems etc.). HADS also has a CID for change over time I believe.