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I don't think granular is the right word here. Android defines something like 150 permissions, so granularity is there.

The issue is (in old versions of Android) you cannot be selective about which ones you grant.

The relevance is that when it comes to transparency, the big dialog of all permissions can disclose a fair amount of detail to the user about exactly what they're being asked to allow.

http://www.idownloadblog.com/2013/02/01/path-ftc-settlement/

I think Apple didn't always have that. There was the Path scandal and outcry that caused Apple to introduce better privacy options.

iOS isn't more granular, it just defers permission requests to the app rather than the app store. In proper practice that app then only asks for permissions when the user is performing an action that requires them, which at least helps the user to understand why they are being asked. Android has now shifted to this model too, but as always, old versions of Android persist.