The choice of target vs query seems like a "commuting" operation a vs b is the same as b vs a but that is not the case. One of your datasets has high information content (reference) whereas the other may be a highly redundant and noisy measurement. The information content in the two files is radically different.

You almost always want to take each one of your measurements and query with it against a reference database. Among many reasons also because blast E-values will be computed relative to database size.