It depends on what sort of depth of field you're after. If you were doing stills, there's very little point as the extra size/weight of the 2.8 IS mk I is only there to get you an extra stop, and that lens really isn't sharp enough to warrant using f2.8. But 1080P is only 2MP, so even the mk I lens will deliver for video at f2.8.
When it comes to shutter speed in video, you'll probably find yourself using an ND filter to slow things down outdoors when you want to use a shallow depth of field with either lens. On the occasions where you do shoot indoors, f2.8 could come in handy - but with such good high ISO capabilities of the 5D3, its not a necessity.