Physical!!!
Physical data is in physical units - kWh, gallons, passenger*miles, kgs, etc
Monetary data is in dollars.
When we use monetary data, we have to guess how much stuff you got for the price you paid, since it's stuff and not money that generates emissions. As you know, as purchasers of stuff, it doesn't always cost the same amount.
Physical data is more precise because we know exactly how much you consumed and we have to do less modeling.
Plus our list of physical emission factors is much more precise and specific.