Same protocol, different frequency. So why does 802.11 spec not take advantage of the higher frequency to obtain higher data rates?
Keep in mind that a higher frequency doesn't translate to moving data faster, rather it is the modulation of the signal that determines that data rate. The 802.11n standard either requires or makes optional the same set of major features and modulations in both frequency ranges.
However, that being said, there are a number of best or common practices that typically will make 5GHz faster than 2.4GHz.
First, there is an option for channel width, either 20MHz or 40MHz. In 2.4GHz, you only have room for one non-overlapping 40MHz channel (in most regions). To reduce co-channel interference, you need at least three, so this option is generally not used in 2.4GHz. In 5GHz where you have many more non-overlapping channels available, this isn't a concern and 40MHz channels are the norm.
Second, is the guard interval. 802.11b/g used a longer guard interval than 802.11a. 802.11n makes the short guard interval an option in 2.4GHz, but this is still often left as the long guard interval since some older devices have issues with a shorter guard interval. Deployments in the last couple of years are more likely to enable a short guard interval on 2.4GHz, but this still seems to be in the minority.
These two factors alone account for over twice the performance between the two frequency ranges in a normal deployment.
From there, it is not at all uncommon for enterprises to turn off any legacy support in 5GHz and run it in a 802.11n only or Greenfield mode. Not having to allow for older 802.11a devices can further increase performance. The reasoning behind this decision usually follows that the majority non-802.11n devices did not support 802.11a (5GHz), for those that were dual band, the 2.4GHz band still exists for them to connect.