There is little doubt that electrolysis works better than laser removal, but honestly even though it might take many passes for people with light skin and dark hair the results can get to be the same, at least it has on some people I know (I have not done laser, but I have done eletrolysis)
Less effective or not I am still looking into laser as electrolysis is painful, I mean very painful. It does however depend a great deal on where and how it is done though. I hear that laser is more like a rubber band snapping at your skin, which sounds like a nice European vacation vs using electrolysis on my upper lip area!
Price really depends on how it is done, if it is in the home electrolysis is very much cheaper, I bought my unit for $8 new from ebay, home laser starts at $100. As far as professional rates; laser is probably cheaper most places, but I suppose someone could charge very little for electrolysis and make it cheaper but, I doubt it.
The real difference comes down to this, laser just doesn't work well for some people. If it works well for you, then it is probably better. If it doesn't work well I wouldn't push it as you could destroy your skin pigment, in that case electrolysis is a better option.
Since you asked how they work, laser attacks the pigment in the hair, hopefully killing it. Electrolysis sends an electrical charge at the base of the hair and destroys it.