When to use Da or u for mass units
It doesn’t matter. Both units are basically identical, much like there is no everyday difference between the units mbar and hPa. There may be situations where one is preferred — e.g. hPa are, in my opinion, rarely used outside weather reports — but they should be understood nonetheless.

If there is anything to be said about the two, it seems using dalton is more popular in biologic contexts. But that wouldn’t be a tendency to base anything on.

Being consistent within one’s lab, within the journal one is publishing in or throughout one’s thesis is far more important.