Only saw this now. Here's an older answer of mine, where in the beginning I talk a bit about structural differences between the early British and Spanish empires. The second part deals more with discourse of empire and rule. One major difference I don't mention there is the difference in administration, with the development of Viceroyalties in Spanish America that had quite a few liberties vis-a-vis the far-away Spanish Crown; and the building on indigenous political organisation at least in some Viceroyalties. This model wasn't followed quite in this way by later empires with their more "modern" bureaucracies.

The book I mention in the post, Pagden's Lords Of All the World, might be interesting for you. It goes into more detail on how the French, Spanish and British justified their empires, and early modern times and beyond, and how interlinked their justifications were. Another interesting work is Anthony Marx' Faith in Nation, which looks more at how a national consciousness developed in these same states in early modernity -- although with from a more European vantage point it's an interesting base to start from. Let me know in case you want more sources especially on Spanish America.