There are two comparative books on those three empires: Stephen Dale's The Muslim Empires of the Ottomans, Safavids and Mughals and Douglas Streusand's Islamic Gunpowder Empires: Ottomans, Safavids and Mughals.

I wouldn't rate Streusand's book very highly; he's not (IIRC) a historian, and the book is a bit popular and obvious in his comparison. Dale's book, however, is much better. He structures the book as an exercise in comparing the experiences of the three empires on various aspects: their origins, economic life, imperial cultures, and so on.

It gives you a good comparative look at the Mughals (in which Dale is an expert) and the Ottomans (where there exists a well-developed and accessible historiography on numerous areas). It is less good, however, on the Safavids, with things like an old-fashioned notion of decline theory, an overemphasis on the achievements of 'Abbas, and things of that ilk. It's certainly not bad, it's just a natural consequences of the often understudied and obscure nature of the field. Dale is pretty good on the economy, though, reflecting his own role in overturning old notions of the decline of the overland trade and the importance of Europeans. (See his Indian Merchants and Eurasian Trade for more).

I can't really recommend any other general works on the Safavids because there isn't really a suitable one; Savory's Iran under the Safavids was excellent in its time but is now woefully outdated, while Newman's more modern Safavid Iran: Rebirth of a Persian Empire is nominally an introductory work but is one of the most tortuously written, selective and iconoclastic works I've ever encountered, so I can't really recommend that either. There are good broad-works on aspects of the empire (the economy, religion, &c) but no good general work on the Safavids as a whole, I'm afraid.