I think they are both assimilated well, I would use both powder and also fresh.
Fresh tumeric can be finely chopped/minced and added to curries, soups, stir-fried veggies, or whatever. Or chop a piece and add it to a fresh vegetable juice.
I think in terms of Ayurveda, tumeric comes under bitter taste, and ginger is pungeant taste, so I would use both - we need all tastes for balance. I like tumeric around lunch time, and ginger either in morning or evening. they are both good, in terms of anti-inflammatory, and antioxidant properties. and ginger has warming quality, nice in cooler weather.