Hi @iordanis,
If your goal is to compare these data sets together make sure that all of the amplicons are over the same exact after your primer removal. This is becuase, your data will be of different lengths.
Correction. These are both V4 primer pairs... the first pair reports the reverse primer in the reverse complimented orientation:
That is the V3V4 primers ...
GTGYCAGCMGCCGCGGTAA forward
ATTAGAWACCCBNGTAGTCC reverse
... will longer fragments compared to the V4 primers:
GTGYCAGCMGCCGCGGTAA forward
GGACTACNVGGGTWTCTAAT reverse
See later post about the correction.
So you should trim the V3V4 reads down to the V4 read length after primer removal. Actually, you can likely just use cutadapt to trim / extract the V4 primer region for all the data sets. Then I'd use the V4 classifier.
But be cautious. Even after you trim the data to cover the same region (i.e. v4), there will still be PCR amplification biases present within the data. See this post, and this post with references.