One would guess that the State of Florida had more funds available for general purposes like the state archives. It's unfortunate that records similar to those available at the Alabama Department of Archives and History aren't accessible.
As for resource overlap, it's much less than you might think. Mobile and Montgomery newspapers (and there were several in both cities) do cite events involving early Alabama military commands at Pensacola, and sometimes reprint articles from Pensacola newspapers. However, the directory for newspapers at ADAH lists only Alabama holdings. As for military service files, these are not available for Alabama soldiers, the same being true for troops from Florida. Florida pensions on line are much more accessible than Alabama Confederate pensions.
For events of late 1860 and early 1861, a researcher would want Governor Perry's papers, commissions and orders issued, and papers of other state departments. They must be somewhere.