Oil heaters by far are more cost effective and safe. Oil heaters do take longer to heat a room but will provide you a more comfortable heating experience. Also the size of the room is a factor in cost efficiency.
Oil filled units are the most efficient heaters. They use a heating element in a bath of oil. The oil stays warm in it's container and heats the surrounding air. The big thing to know about oil and water filled heaters is that they are sealed units so you do not need to worry about spills or refilling fluids. Once the oil or water is heated the element cycles off and on enough to maintain your desired temperature.
"Heating your home with electric space heaters can easily double or triple your
electric bill if you are not careful. Even though they are typically small in size,
and often touted as 100% efficient, electric space heaters use a lot of electricity.
Most space heaters use on average 1,500 watts of electricity and cost about 15¢
an hour to operate. While that may not sound like much, it can add up quickly
if heaters are left on for several hours a day. Leaving one space heater on for 8
hours a day for a period of one month could easily add an additional $30-$40 to
your monthly electric bill."
[http://siliconvalleypower.com/modules/showdocument.aspx?documentid=9223|SPACE HEATER GUIDE Energy Saving Tips]
Hope this helps.