Hi, eklektica

-- you didn't mention what areas or how much excess hair growth you are concerned about, but I will just say from my experience in receiving both types of hair removal, unless you have only a very small number of hairs in a very limited area, I would strongly recommend LASER as the best method of hair removal. I found it works MUCH faster and was more effective long-term than electroloysis.
Unfortunately laser doesn't yet work well for some groups of people -- apparently works best if you have a lighter skin and a darker hair color because the contrast is what the laser beam uses to be effective. Also they warn you that laser does not work at all at this point on white or gray hairs. So in those cases maybe you are stuck with electrolysis. (But they are developing new lasers all the time to try to overcome those limitations.)
I am sorry to offend dedicated electrolysis workers as I know it is their livelihood and I greatly sympathize as I sometimes worry that my own work skills (not related to hair removal) could become obsolete, but I suspect that method should and will soon become more and more outmoded. (I say this only as a customer's opinion, not as a knowledgeable expert in either field; I certainly may be missing part of the picture and willing to be corrected.)
But basically what I personally found was the LASER spot (couple of inches or so, they do overlapping circles till they've covered the whole area with the hair, exact size of the beam varies with the model of laser) hits HUNDREDS of tiny hair follicles in its single round "blast" area. Whereas in the ELECTROLOYSIS process, the needle had to be inserted into A SINGLE FOLLICLE AT A TIME, the "blast" of current then gets sent into that single follicle, they remove the needle, re-insert into a single different follicle, etc.
So obviously electrolysis will be an infinitely slower process, covering a much tinier area per session. And this effect is multiplied because in either process there is no guarantee a particular blast of current will succeed in destroying a particular individual follicle it's aimed at; sometimes a follicle has to be re-blasted two, three or more times if the amount of current was wrong for whatever reason or just because that hair was a sturdy little sucker

. (BUT, to add to our woes, the hair follicle may be damaged so sometimes it will grow back crooked trying to get to the surface, causing ingrown hairs, raised cyst-y things on the skin and other lovely stuff you get to endure till the process is over...yarrgh...) AND, since hair always grows back in its own long individual cycles which you can't control, months later you may be sitting there trying AGAIN to get rid of the very same individual hairs, one by one by one...
Anyhow, my bottom line: after a lifetime of excess hair and struggling with uncomfortable, unpleasant methods including shaving, waxing, electrolysis and trying to pretend it didn't matter

, five years ago I had my chin, upper lip and arms (which I felt looked like a man's) done with laser. I needed a total of maybe six or eight 15-or-so minute appointments (it was an expensive clinic, appts. cost maybe $200-400 or so per session, depending what areas that day) which could only be done as the hair grew out, so over a year or year-and-a-half or so (as I said, you have to wait for the hairs to come in, in their own cyles which take months at a time -- it's not the same hairs there all the time even though it may look they are -- the individual hairs are constantly growing, falling out and being replaced by hair growing in microscopically close follicles at different cycles).
So, obviously, even with laser, bring lots of patience and money!!

Yes, it's expensive, especially for a really skilled operator, but I guess it depends on what is important to you, and what you want to save and use your money for.
Now my laser hair removal is done. It is one of the best things I ever did for myself. I go back every six months to a year for one 10-or-20 minute treatment and am virtually hair-free in those areas. It has been a joy to feel normal for the first time after a lifetime of self-consciousness and wasted time and discomfort with ineffective temporary methods -- I hate to even think about all those years and unhappiness.
But very important, whether you choose laser or any other method, PLEASE BE SURE YOU ALWAYS GET AN EXPERIENCED, SKILLED AND QUALIFIED/CERTIFIED OPERATOR, preferably a nurse or MD if you can. Your skin can be seriously damaged if they use too high a current or make other mistakes.
By the way, I am aware that electrolysis operators are allowed to call their process "permanent," whereas laser operators can only call it "long-term" or something to that effect. However, in reality I think both treatments may or may not succeed in killing each individual hair root (often NOT), but I found laser worked much more quickly and effectively long-term because it could repeat the process (re-blast the hairs that had not been successfully eliminated the first time) so much more quickly and efficiently. (because of the large number of hairs under each blast of the laser beam instead of just one hair at a time as in electrolysis.)
I offer this experience only hoping to be helpful. I suffered so much and so long with excess hair growth and until the laser became available I really had no good solution...hope you get your excess hair issues taken care of as early as you can in your life with whatever method you find works best for you.