Hello Nir,
If you used the same input files but different taxonomy assignment methods or databases, this could dramatically change your results! However if you use the same taxonomy assignment method and same database with dada2 ASVs and Qiime 1 OTUs, the overall taxonomic composition should be very similar.
Every step in the pipeline matters, so keeping track of each step when comparing results will help you identify which step is changing results the most. Here, my intuition is that the taxonomy assignment of Qiime 1 and Qiime 2 is more different than OTUs vs dada2, but you would have to try it to see.
Colin