The .cel files are the almost-most-raw intensity data, and contain the probeset-level intensities from the array. So (for example) if there were 11 probe-pairs per probeset on the array, the .cel file would contain 22 intensities per probeset.

According to the GEO page you linked, the data table at GEO shows GC-RMA signal intensities derived from the .cel file by the original authors, one summarized log2-scale intensity per probeset. This is the 'processed data' and it should be suitable for differential analysis.

The output you generated is of course RMA, one log2-scale summarized value per probeset, which is a different summarization method compared to the GC-RMA values that you see in the GEO table that the original authors generated, so you'll get different numbers. For more details on the differences between RMA and GC-RMA you can check the corresponding publications.

If you are comfortable with using GC-RMA as submitted by the study authors, then for gene-level differential analysis, you don't need to retrieve the .cel files and reprocess them using justRMA(). Instead, you could download the GC-RMA tables provided by GEO and analyze those GC-RMA values directly. Unless you are doing something unusual, or have a good reason to do otherwise, that's probably the simplest and best approach for your differential analysis.