Load times and other aspects of data access are typically A LOT faster when accessed from a hard drive though. That is why installed 360 games show better load times as well as PS3 games. Blurays have a very slow read rate compared to HDDs and can hold a lot more data than DVDs, hence why a lot of games need to have mandatory installs.
From what I can read a bluray has a max read rate of 9 MB/s on the PS3's 2x drive. While even the launch 60gb 5400rpm HDD can read around 24 MB/s on average. This is just what I could find in a short search. From the bluray site faq and PS3 wiki.
So HDD read rates are faster, almost 3 times faster on average than even the blurays max read rate.
This is just read rate though and I am unsure of the exact numbers or data to memory. But in practice it seems that games accessed from the HDD do load faster so would indicate that the data to memory is faster on HDD games. There have been a few cases though of this being backwards, as in Halo, the disc was optimized for DVD drives and as such when that data was installed onto a HDD the loads were worse since Bungie didn't account for this since installing discs on 360 was not a feature at the time. The game would cache data on the HDD and its faster for data to go from disc to HDD than HDD to the same HDD.
I don't know how The Show uses its data though, but having a mandatory 5gb install and optional additional 5gb, I would assume having that data on the HDD would be beneficial. Again I wont say where or how, but there are ways to test this.
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