I think the only answer anyone can give is "it depends". There is no single authoritative answer regarding laser, hence why the US FDA does not list it as "permanent hair removal" and instead classifies it as "hair reduction".
There are a number of problems. First you need to be close to an ideal candidate - light skin, dark hair. Second, even some ideal candidates can't permanently remove facial hair this way. For them, it just doesn't work.
However, laser is a lot cheaper than electrolysis, so if you want to give it a go, then do so. Maybe you'll be one of the lucky ones! And if not, you can always start on electrolysis later.