It is certainly possible — and in fact you can use the data provenance to confirm that you used the same exact steps. The read extraction and classification steps are not random, results should be consistent if you have identical classifiers.
Want a great way to quantitatively compare these? Use qiime quality-control evaluate-taxonomy — it will compare the annotations for each individual sequence, and look at the correlation. If you get an error then the accession IDs must be somehow different even if the content is not...
So the question, I suppose, is really why you are getting so many unclassified reads? Start here: