Hi,
I'm not sure what SpeedSeq does, but any kind of recalibration is likely to change the output of Platypus, particularly if base quality scores are modified. Simple de-duplication should not make a difference, as Platypus will remove duplicate reads anyway.
I would expect the changes to occur mostly in low coverage regions, or around sites which have weak support for variation. If some variants are present in one file but not the other, it is probably because they are at the boundary of what Platypus will call, and these are probably not very trustworthy. Genotype differences may occur if a small number of reads have been removed, or had their base qualities changed, or been modified in some other way, but this should only happen if the original genotype call was not very clear (e.g. an 8/2 ref/variant split might get called het in the raw file, but if the 2 variant bases are recalibrated to lower quality then this might become hom ref).
As for which is more reliable, well that depends on whether SpeedSeq is doing anything sensible or not. It is certainly possible to improve calls like this using population information and a well-implemented recalibration.
To be honest though, ~300 variant calling differences out of 3 million is not a lot (0.01%), and the false discovery rate among both call sets is probably much higher than this (> 0.1%), so I suggest checking a couple manually to see what the differences are in the 2 BAMs and then not worrying too much about it.
Kind regards,
Andy