Re-reading your question, it sounds like you want to compare a gas fireplace with an electric heater. In other words, place a radiant electric heater next to a gas fireplace - how do they compare: heat vs. energy?
BTW, I always think in terms of 3.41 Btuh = 1 Watt (the reciprocal of the conversion posted above).
You may use the conversion, as long as you're comparing electricity in Watts to Btuh's in fuel burned (NG). Natural Gas is sold in units of Therms (100,000 Btuh), and has an effective specific heat of combustion of 1000 Btuh per cu. ft. You may be able to derive the number of therms or Btuh's burned by watching your gas bill + fireplace burn time, or perhaps the gas fireplace mfr has a fuel consumption rating.
Efficiency is the important factor, though. A radiant electric heater may approach 100% efficiency - Watts of electricity into the electric heater equals Btuh's of heat output. However, a common fireplace - even one with natural gas - is horribly inefficient: on the order of 10%. Without a heat exchanger to transfer the convective heat, most of the heat generated from burning the Natural Gas goes right up the chimney. What's left to heat the space is only radiation from the flame.
Even so, the 100% efficiency of a radiant electric heater pales in comparison to the COP of a heat pump. (In fact, it could be described as a salesman's trick.) Heat pumps use the rejected heat from trying to air condition the infinite sink of outdoor air. COP's with heat outputs of 3 times the electric power input are common.