There are a lot of parallels. They're both proprietary software packages designed to be used by developers to implement things. Where the parallel breaks is that for some reason, some here (I won't mention names) seem to think that Mantle isn't proprietary, and that AMD isn't itself doing the things it's whining about Nvidia doing.
The reality is that they're both doing it, and it's fine. It's how competition works. It's how new products actually get into our hands.
But the idea that when Nvidia does it they're this evil horrible money-grubbing corporate empire that's out to hurt everyone but their pocketbook while when AMD does it it's just this grand conspiracy to make AMD look bad and they're really the savior of all gamers everywhere is just absurd. Yet, that's what gets attention.