Some of the details will be the same, but there's always the possibility that different individuals provided testimony or that's just more detail in this application. No matter how you define an "exhaustive search," getting the bounty land application is necessary--even if the pension has already been obtained.
The warrant shown in this illustration was located on the Bureau of Land Management website, by searching for warrants issued to Randall F. Fugate. Searching for miltary warrants on the site is something I do for any Revolutionary War or War of 1812 veteran. Fugate's was issued in the 1850s, long after he was dead. A patent was eventually issused for property in Missouri based upon the warrant. The Fugates never settled in Missouri. Eleanor Fugate sold the warrant to a man who eventually patented the property. When searching the warrants, remember they could have been issued long after the veteran was deceased and for property in a location where the family never lived.
The warrants are at the National Archives in Washington, DC. We will have an update when copies have been received.