It's like anything electrical really, it depends on the kilowatt (kWh) rating. The higher the value, the more it'll cost to run, as it uses more electricity. So, if you've got a 1.5kW heater, and your electricity unit rate is say 16p per kWh, the heater will use 1.5 kilowatts for each hour it's on - that's 24p for that hour.
Re which is better, it really depends on what you want to heat. Halogens produce a direct heat, pretty much heating only what it's near, and they heat up quickly. The plus side to halogens, is that if you're sat near them, you feel the benefits quickly, and you'd probably be more inclined to turn it off if you get too hot. Chances are, by doing this, you'd be using less electricity. Oil filled radiators are slower to heat up (so they take longer to cool down, so you get a bit more residual heat for a longer period of time), but do better at heating the air, therefore the room - you don't really get this with halogens. If you want a heater to heat the room or large area, i'd say go with oil filled :)

Oil filled for good low level background heating, but if you need a quick blast when coming in from the cold especially if you are wet, you can't beat a little fan heater, which you can also raise up onto a counter and/or angle to blow warm air at you.
Mother's kitchen is unheated and it's like the arctic, after last year when she refused a fan heater from Freecycle point blank, and THEN we got months of snow which was unheard of in this area, I'm not freezing my posterior off out there again, I do all the cooking and at times I could barely feel my fingers enough to make a cup of tea.... Never again!

Halogen heaters are EXTREMELY expensive to run, and do not throw out much heat. You have to have them right next to you. They also break quickly. At one point when we foolishly thought we could save on oil we used halogen heaters -we had four in total and the electricity cost for 24 hours was over over £10 just for them! In the end what saved us MASSES of money was a new boiler, as the oil lasts much longer than before with the old one. (The old one was nearly 40 years old.) We bought 500 l of oil in March, used the heating in March and probably a bit in April, then since September on and off, in October pretty much all the time, and of course it also heats the hot water for 14 hours a day. We have STILL not run out -with the old one we'd have run out about July when the main use was for water, with heating on 500 l lasted 4 weeks max.
Oil filled radiators also cost more to run in electricity costs than using the oil central heating.
If its for your bedroom I really wouldnt go for a halogen heater, its too much of a fire risk imo. If you can be there/awake to make sure nothing falls on it, it falls over, the duvet falls off the bed knocking the heater over etc..
Id go for an oil filled radiator with a thermostat so you can regulate it, perhaps put it on a timer so you can have it going an hour before you go to bed then turn off about two hours after you go to bed (so you will be asleep). Then you could always have it coming on an hour before you wake up perhaps?