Is there much difference as far as gene annotations between these two genome assemblies (Grch37 and human_g1k_37)? I am primarily looking to make sure the ensemble GTF file with the annotations for differential expression will work with either assembly when reads are mapped to it.
this is not correct. the main thing to check is that the reference you're using is exactly what you think you're using. historically, american projects tend to use chr-labeled cromosomes, wether european projects tend to use non-chr-labeled chromosomes. and this hasn't to do with the reference genome of choice.