THE ANSWER
It depends on your hair colour and your skin tone, more than on price or speed. Laser is faster over large areas of dark hair on lighter skin. Electrolysis is the only method recognised as permanent, and the only one that works whatever colour your hair is and whatever tone your skin is. For a lot of people the sensible answer is laser first on the dark hair, electrolysis to finish. For anyone with light hair, electrolysis is the only one of the two that does anything at all.
Why
The two methods work in completely different ways, and that difference explains everything else about them.
Laser sends light into the skin that is absorbed by melanin, the pigment in hair. The absorbed light becomes heat and damages the follicle. This is efficient because a single pulse covers many hairs at once, which is why laser is fast over a back or a pair of legs. It also means the method has two hard requirements: the hair needs enough pigment to absorb the light, and the surrounding skin needs to have enough less pigment that the energy goes into the hair rather than the skin.
Electrolysis puts a fine probe into the follicle alongside the hair and applies a current there. Nothing about it involves finding the hair by colour. That makes it slower, because it treats one hair at a time, and it makes it indifferent to hair colour and skin tone.
The regulatory positions follow the mechanisms. Laser is cleared for permanent hair reduction, meaning fewer hairs. Electrolysis is recognised as permanent hair removal, meaning the treated follicle stops producing hair.
Is laser faster than electrolysis?
Yes, considerably, over a large area of suitable hair. A laser pulse covers a patch of skin, while electrolysis treats individual hairs. If you have a full back of dark hair and lighter skin, laser will get through it far more quickly. That advantage disappears entirely on hair laser cannot see.
Is electrolysis cheaper or more expensive than laser overall?
Per hour, electrolysis usually costs less than a laser session, but it takes many more hours, so a large area generally costs more overall. On a small area, or where laser would leave hair behind and need finishing anyway, the comparison narrows or reverses. Compare total cost to your goal, not price per appointment.
Can I combine laser and electrolysis?
Yes, and it is a common plan. Laser clears dark hair over a large area quickly, and electrolysis handles what is left, which is usually the light, fine or grey hair. Nothing about electrolysis requires you to have avoided laser first. See electrolysis after laser hair removal.
Why do most places offer laser and not electrolysis?
Because of the economics. Laser treats many hairs per pulse, so a provider can serve more clients per hour, and one operator can handle large areas quickly. Electrolysis requires an appointment per client for hair treated one at a time. That is a harder business to run and it is why dedicated electrolysis practices are much rarer than laser clinics.
What the evidence says
The FDA and the American Medical Association recognise electrolysis as a permanent method of hair removal. Laser devices are cleared for permanent hair reduction. Those are different regulatory claims describing different outcomes, explained further on permanent removal vs permanent reduction. The pigment mechanism behind laser is not disputed, including by laser providers themselves.
What to do next
Work out two things before you compare prices: what colour is the hair you want gone, and how big is the area. Those answers decide the method far more than cost does. If any of the hair is white, grey, blonde or very fine, laser will not treat it, and that part of the job needs electrolysis regardless of what you do with the rest.
Laser is not part of this service, so this comparison has nothing riding on your answer. If your hair and area genuinely suit laser, that is worth knowing. If they do not, see gray, white and blonde hair removal.