I've had both electro and laser on my face, as well as near full-body laser hair removal... based on my experience and research one thing of huge importance is the experience and training of the tech. A great laser tech will get you far better results than an average electrolysis tech.
Also, stay away from the "Laser Centers" and all-in-one spas that sell laser, waxing, tanning, etc. They really lack trained staff. The place I go for laser is a doctor's (Plastic Surgeon) office and the laser tech is a PA (physicians assistant) who is certified in my state for laser... not just a cosmetologist etc. Yes it's very expensive, but faster and seemingly permanent for me, and finally the results speak for themselves. Make sure the person using the laser has been properly trained and is preferably a RN or better.
As far as lasers go, there are main flavors. The 2 most popular are YAG or Alexandrite. The YAG works better for people with darker skin, and the Alexandrite better for people with fair skin. The darker the hair and fairer the skin the better the overall result.
Electrolysis is more dependent on the operator and their training. It's very hard to find a good one. So ask around and preferably try to find one with MTF or at least some sort of male clients. This is really a dying profession which is mostly been supplanted by laser. If you feel the hair being pulled or any resistance to being plucked after the needle has been inserted, the tech is not doing it right. Go elsewhere, as the hair will return. The hair should freely slide out after being zapped. I think laser first, followed by electro to clear up any stragglers is the best approach... but this will vary by individual, skin & hair color etc.