Unfortunately there's no clear answer for all of this... but here is what I know. Hope it doesn't confuse anyone more than they already are!
I did laser for a year before switching over to electrolysis. It was actually my electrologist who suggested I do it this way, and I'm glad I did.
Laser sometimes works well and can indeed be permanent. It honestly depends on your skin color, your hair color, the skill of the operator, type of laser, etc. Light skin and dark hair is the best. If you're dark skinned, I'd forget about laser; same if you've got a light colored beard.
My electrologist has been working with the TG community for 20 years, and she said that in her experience, laser seems works well on certain parts of the face, but not others. For me, it worked well on the cheeks and neck, but not around the mouth/upper lip/chin area. I hear this is kind of common for it to not work as well in those areas, probably due to the coarseness of the hair in those areas.
It's been over a year for me now, and although not successful on the upper lip/chin, none of the lasered hair has grown back in the areas it was successful. I'm assuming that most of it won't grow back.
One thing about laser is that it needs to be done on a regular basis, every 4-6 weeks or so, to catch all the new growth cycles, but also to constantly keep pounding the hair follicles until they give up. In the words of my cosmetic doctor... "Hair needs to be kept beaten up." If you wait too long, the follicles will recover fully from their weakened state, and you're starting from scratch again. You want to keep them under stress until they give up. So, there's no having a laser treatment and then waiting three months for your next one. You need to go religiously, or yes the hair will recover and grow back.
Electrolysis works the best, but it's tedious and slow, not to mention more expensive, and PAINFUL if there is no anesthesia of some kind. Your mileage may vary, but I'm the type of person who jumps off the table simply on the insertion of the probe into the follicle, before the zap even. If you find that you can't take the electro, see about numbing creams, or injections to numb the face. For the upper/lower lip and chin (some of the most painful areas) I usually see a dentist and have a series of injections to block the nerves and numb the whole area. Six or seven mildly uncomfortable shots in the mouth, and I'm sleeping peacefully during a two-three hour clearing session. And, it's saving me money, because my electrologist can work faster when I'm not jumping out of my skin.
Also, it's possible to mix the two, if you've got the cash. Go for laser session, wait a couple of weeks for all the affected hairs to fall out, then go for an electrolysis session to grab the ones that didn't respond. Wait a couple more weeks for your skin to heal, then you'll be ready for the next laser session, and so on.
I suppose if I had little money, and didn't need to worry about passing, I'd just start plugging away with electrolysis as I could afford it. That way there's no sticking to any sort of rigid schedule, electrolysis could be scheduled here and there as funds allow, and the ones you zapped shouldn't grow back at all. On the other hand, laser is cheaper for large sessions, zapping the whole face and having the hair fall out at once can improve passability, and if one has the cash to keep going, might work well if done consistently.
All of our situations are a bit different, so I suppose a good solution is to take into account personal and financial situations, and make a decision based on those factors.
Hope this helps a bit...
