how do convection space heaters work compared to radiant heaters, which is better to heat a room?

Answer 1

Convection heaters heat air, which in turn heat surfaces, slowly.

Radiants heat surfaces, which heat the air even more slowly.

I prefer convention, because the heat is distributed more evenly, and doesn't fry the side of your face that is facing the heat source.

Answer 2

A convection heater heats air which is released and rises thus drawing in cooler air near the floor to be heated.
A radiant heater has glowing rods which give off infrared radiation which travels in straight lines to heat the surfaces or people that it hits.
An other choice is a force air heater which has a fan to blow the heated air.
Most people prefer a radiant heater for personal heating as it puts the heat where it is aimed (at the user) and is silent. For room heating, a convection or forced air is better because it does a better job of providing even heat - there is not a cold side as with radiant.