My preferred method is to teach the dog to give into leash pressure. It doesn't matter if the leash is attached to a harness, collar, or whatever, you teach that hitting the end of the leash is a cue to give into the pressure.

This is particularly important because dogs, like most mammals have what's called "oppositional reflex" where their natural response to being pulled one way is to want to pull the opposite way. Can happen with pushing too. Anyone who has had a horse push them into a fence or barn wall and tried to push back will know exactly what this feels like. Same happens with pulling.

To counter this instinct, you teach the dog to give into the pressure instead. This video is for fearful dogs, but the principles of teaching the "give" apply to any dog:

I also like teaching the dog that when my feet stop moving, that too is a cue to return to me.
And I teach a lot of loose leash walking with the dog off leash by encouraging check-ins and staying aware and engaged with me.

 

Cosmos laid it out well. But gear-wise, a harness is safer for the dog.

 

If you do use a harness, you can get one that has an attachment on the front, on the dog's chest, as well as on the back. The front attachment of the leash makes it very difficult for the dog to pull. It is not a solution in itself, but can be a training aid. My young dog doesn't generally pull on the leash because I have trained him not to.....but he still has a very high prey drive and when we are walking every day out in nature he sometimes forgets and starts to take off after something. This is just his instinct, and I don't blame him for it but I don't want him to do it. When he does that, I stop and move the leash from the back of the harness to the front and leave it there for a few minutes to remind him that if he wants to pull we can go back to having the leash on the front, which he does not prefer. After two or three minutes I put it back on the back of the harness. I do it without any scolding, of course, and I am always gentle with him. Over time this has greatly reduced the number of times he tries to take off after something, and I often I can see him start to do that and check himself before he reaches the end of the long lead. Of course when I see him do that he gets praise and a biscuit.

 

Anti-pull harness vs slip lead to teach the dog not to pull? I'd say the answer is neither, if your goal is to teach the dog not to pull. Both devices have their place when you need to use them short term for safety reasons. I keep a slip lead in my car in case I find a loose dog that needs to be escorted home. It's easy to get a slip lead onto a dog, and it's difficult for a dog to wiggle loose from a taut slip lead. An anti-pull harness can help with a large dog that forgets leash manners.

However, neither device will actually train the dog not to pull. Gear does not train dogs. Training trains dogs. Eventually the dog becomes habituated if you rely on the devices without adding in training. One of the dogs I had years ago would walk down the street, pulling, even as her tongue turned blue from her nylon slip collar. Another one of my dogs learned to spin around and run backwards while wearing a front clip harness. I think the video link provided by @cosmos has some good tips, especially if you are working with a dog that is nervous while on leash. I would add two things to the training however.

One is the concept of walking at heel. I teach this two different ways. One is to work with the dog off leash (though a long line would also work.) I amble around, letting the dog follow me if he wishes. As soon as he happens to wander into heel position, I click and give him a treat. I then resume walking. When the dog falls into heel again, I give another treat. Pretty soon the dog is following me like a shadow, hoping for more treats. At that point I make the game harder with speed and direction changes. Each time the dog slides back into heel position he gets another click and treat. The other way I train for heeling is to start by teaching Touch. Then I use Touch to lure the dog to my side. I reward him randomly for staying there. Each time the dog drifts away I request a Touch to get him back to my side. Both these games teach the dog that heel position is a good place to hang out, because dogs walking next to me get fed treats.

The other is to use access to interesting things as a substitute for food rewards. Often a dog will try to drag you towards an interesting scent. Unless the dog is exceptionally food motivated, at that moment they probably think the scent is more rewarding than a training treat. So I look where the dog is looking, and I stop moving. I wait for him to stop pulling. Then I take a step towards whatever caught his interest. I stop again if he pulls. I keep walking if he gives me a slack leash. Each moment of slack leash gets him closer to the thing he wants to visit.