Hi @kevin_SalOrt,
I think you meant to say that you used GreenGenes (13_8 & 13_5) and version 138.1 of SILVA. 
Can you provide more details about the sequences you are trying to classify? Are they full length sequences? A specific amplicon region, i.e. V4, V1V3, ...? What approach are you using to classify your sequences, classify-sklearn?
You can always use RESCRIPt to construct and optimize your own SILVA classifier.
How are you selecting your manual BLAST results? Taking the top hit? If so, be wary of that approach as quite often the top set of hits are equivalent and they are not necessarily sorted in any particular order. For example, your top ten hits can be exact matches to several different species or genera. In some cases the top few hundred hits are equivalent, and any hits to different taxa would go undetected unless you manually scroll through a few pages of top hits. This is quite common with short amplicon sequences, and precisely why the consensus-blast, and consensus-vsearch methods are provided.