EnergyNumbers has a good answer (+1), but why don't you measure it and let us know?
Of course "efficiency" is a little ambiguous. Green house gas production? Just your $$? The latter is easier, the former changes over time.
Get one of those power meters for the plug and see what it uses overnight. Most space heaters are ~1500 W, which is a lot. Your power bill has the rate and distribution costs.
The natural gas for the furnace is a little tougher. But you should have a monthly history. You can see when you turned your furnace on for the winter. If you have other gas appliances, then subtract the previous month and call the rest your furnace. E.g. turn on furnace in October, so subtract what you used in September and call the rest your furnace use. Take your winter monthly bill, subtract this base-use, divide by 30 (days/month) and that gives your daily cost of your furnace. You probably turn your heat down at night for sleep but also while your out during the day. It might balance out so call it 1/3rd at night (8 of 24 hours). (Maybe it's 6 hours of sleeping (1/4th), but with the furnace down you use it less, but it's colder at night - it probably all washes out).
So 1/3rd (or 1/4th) of 1/30th of your monthly winter gas bill (minus base use) vs. average (multiple measurements, please :) of 1 night of powering a space heater.
Again, if you're measuring $$, don't forget distribution charges, etc.
Normally I'd just say turn the furnace down and use a heavier blanket with thicker pyjamas and call it a day. But old houses can be leaky, and they leak faster when they're warmer (rate of heat transfer is directly proportionate to the difference in temperature). I have an old house and until I finish renovations, it's leaking heat in the winter. But you can seal windows in the winter (plastic cover) for rooms you don't use, etc. Plus I notice my furnace goes on more if I turn my furnace fan off at night because all the heat migrates upstairs and thermostat is on the main floor; it's more efficient to leave the fan on.
Mostly I want you to measure it and let us know. :)