My preference is to brief from the FMC, as this is what the aeroplane will actually do, whilst continually referring to the plate. It also ensures that everything is covered in a logical order. This may vary between types but for me on the Triple, this is the order:
1. Legs page (covers STAR, Approach and G/A in order).
2. This prompts you to check for minima and Aa.
3. Vnav descent page (Mach/speed during descent, wind, transition altitude and MSA)
4. Approach page (weights, Vref)
5. Autobrake (prompts you to look at runway length, lights, airfield, etc.)
The above should cover most things. Finally, review using the checklist summary to mop up anything you're likely to have missed.
The main advantage is interaction. Get the other bloke to read the plate while you check the box. Better than the regular drone!