There are a few minor differences between GRCh37 and hg19. The contig sequences are the same but the names are different, i.e. "1" may need to be converted to "chr1". In addition UCSC hg19 is currenly using the old mitochondrial sequence but NCBI and Ensembl have transitioned to NC_012920.
Citing UCSC:
"Since the release of the UCSC hg19 assembly, the Homo sapiens mitochondrion sequence (represented as "chrM" in the Genome Browser) has been replaced in GenBank with the record NC_012920. We have not replaced the original sequence, NC_001807, in the hg19 Genome. We plan to use the Revised Cambridge Reference Sequence (rCRS) in the next human assembly release."