Both Ensembl version 74/75 and version 73 are based on GRCh37, and should also work fine with hg19 - the coordinates should correspond.
Each version of ensembl, which is a set of gene annotations, is based on a particular version of the genome sequence. But ensembl is updated far more regularly than the genome sequence is. There are new versions of Ensembl every six months if I remember correctly. Thus there is no "corresponding GTF" for a particular genome sequence version.
As for your inconsistent results - thats just what happens when annotation versions get updated. Transcript models are retired or added - thus transcripts that were expressed in 73 simply don't exist in 75. Not every change that is made is correct - some transcripts for which you might have very good evidence in your RNAseq, might be removed from one version to the next, but we have to assume the newest version is the best. In the course of a three year project you are going to go through 6 versions of ensembl, and things are going to change quite a bit - thats just the nature of the beast.
The current newest version of Ensembl annotations is version 85, which is based on the GRCh38 version of the sequence. Many people will tell you that you should be moving over to using GRCh38/hg38. However, as yet there aren't any RNA-seq tools that I am aware of that will cope with some of the new features of hg38, in particular the alternative contigs. Thus, if you want to use hg38, you will need to filter out the _alt contigs before you map (or use the "analysis set" from the UCSC website, which already has these filtered out).
You would then be able to use Ensembl 85.