Off the top of my head, I can't think of a paper that shows exactly this.
However, I would probably say that the result will vary based upon what you are trying to do.
The best match that I can think of is what I have done with mRNA-miRNA interactions (unfortunately, none of which has been published yet). The list of genes with targets that have inverse overlap (e.g. miRNA Up, mRNA Down and miRNA Down, mRNA up) are usually fairly different than the genes that have negative correlations between miRNA and mRNA levels (paired for individual samples). You might expect that because you can see a negative correlation among miRNAs and mRNAs but not have the expression levels among the miRNAs and/or miRNAs vary between the two groups you were trying to study.
That said, the difference between overlap and correlation seems to be more similar with methylation and mRNA expression. My guess is that this is because the relationship is 1:1 for methylation:mRNA but not miRNA:mRNA. In other words, the importance of correlation for integration depends highly on the application. Nevertheless, I did show that there is a difference between overlap versus correlation in my COHCAP paper (I am just telling you that I happen to know the difference for miRNA-mRNA intergration is a lot greater):
If you are only working with mRNA, it is a little different story. However, the bottom line is that the tools serve different purposes. Just like the miRNAs, you might have co-expressed genes that don't vary between phenotypes of interest (such as tumor versus normal). I would probably argue that these sort of genes are generally not as interesting, but co-expressed genes will make up a subset of genes used for molecular profiling for subtypes. If you are trying to show that subtype analysis can complement differential expression analysis, you will see lots of evidence for that.
For example, here is one paper (among many) describing molecular subtypes with interesting clinical associations:
This paper quickly comes to mind because I recently published a paper studying the impact of these molecular subtypes on associations with a gene used for immunotherapy (or at least is in clinical trails for such an application):
Hope this helps!