Comparing the gene expression data
There's going to be a batch effect between studies, so unless you have some sort of constant group that you can use for between-study normalization you're going to completely muck up your results from using data from multiple studies.

More specifically, this is what packages like sva and the combat() command in it are used to correct. Note that you should go back to the raw .CEL or .fastq files if you want to process multiple studies, in order to at least ensure that everything is processed in the same way.