Researchers will not typically study batch effects directly if they have another end-point of interest, and may only make a loose reference to batch in supplementary methods. As such, it may be difficult to find the exact experimental set-up that you want.

However, you should be aware that the TCGA has expression data on various cancers as both RNA-seq and cDNA microarray, and, because it's the TCGA, most of these samples will overlap centers and therefore be from different batches. Take a look at the NCI's Genomic Data Commons to see what you can find.

Also take a look at these:

• Large Scale Comparison of Gene Expression Levels by Microarrays and RNAseq Using TCGA Data
• Comparison of RNA-Seq and Microarray in Transcriptome Profiling of Activated T Cells