Have been thinking about this and my brain has come up with the following, which may be 100% bollocks
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Having a look at the specific heat values for various fluids, air requires 1 Joule per gram to raise its temp by 1 degree whereas paraffin requires about double that. So to initially heat the (for example) 1 litre of oil in the rad would take twice as much energy as if it were filled with air. The oil then needs to transfer its thermal energy to the air via convection so you feel a temp change (you'd get some heating from radiation if you were close enough but it wouldn't be evenly applied so probably isn't relevant for this). The transfer of heat from the oil to air must be less than 100% efficient so you've got 'useful energy' losses.
With the fancy fan heater you only have to heat the thin (nichrome?) heating elements which have a much lower specific heat, so you can get the fan heater element up to 25 degrees with much less energy than the oil. However, as soon as you stop supplying power in the form of electricity to the heater elements they'll cool much faster due to their lower specific heat content, whereas the mass of the oil will retain its temperature for longer.
The second (and possibly more important point to consider) is that the heated air will rise if left to its own devices. With an oil rad the air will generally flow directly to the ceiling so you need to heat the entire room's volume of air before you start feeling it at ground level. With a directed fan heater that hot air can pass over you before it rises to the top of the room, so you should feel warmth at your desk whilst the ceiling level air is still cold. Of course, as soon as the fan heater stops you're not getting warm air directed at you so you'd quickly return to the ambient air temp at desk level.
You could perhaps fix this by having a ceiling mounted fan to redistribute the hot ceiling air and force it down to desk height. Given that you're going to be in a fixed position most of the time I'd expect that fan directed hot air would be more efficient so you can concentrate on heating you and not the entire volume of air.
In terms of overall efficiency you need to consider losses in the system - an oil rad needs to heat itself, the housing and then the entire room volume of air before you feel much change. A fan heater needs to heat the element and then the air that passes over you. Intuitively it seems the fan heater would be cheapest as you're ultimately heating a smaller, directed, volume of air.
The actual power rating of the devices isn't as important as the efficiency: if you only need to run a 2kW heater for 10 minutes out of every hour it's going to cost less than running a 1kW heater for 30 minutes of every hour obviously.
I reckon a directed fan heater under your desk blowing at you is probably the best solution. Rapid directional heat, plus the desk trapping some of the air around ground level should keep you toasty and avoid the problem of heating the entire room volume.
I can't see there being much difference in the energy required to heat a whole room via either method. Thermodynamics says you have to provide the same amount of energy to raise a room of volume X by Y degrees regardless of the method and I suspect the two heater methods have similar efficiency in terms of power in and heat out. But if you can just heat the air around you instead of the whole room then you start using less energy.
So I'd probably try a cheapo fan heater instead of the fancy Dyson
PS Sorry this is so long-winded but it's a tiny text box on the iPad and I can't be arsed scrolling back and forth to make sure I'm not repeating myself
