There is really no absolute right or wrong answer as it pertains to many factors. The harness or collar that is considered appropriate has to be suitable for the size and the breed of the cat.
To start with the question of collar versus harness, there are definitely benefits and drawbacks to both. In terms of the collar’s advantages, it is an easy thing to take on and off and the cats generally do not mind wearing a collar.
However, the problem is that if you have a cat that has a tendency to want to pull when they are on a walk, a collar puts a lot of strain on their neck and overtime can potentially cause injury to their neck.
So you need to read carefully about different types of collars before making a decision to purchase one. When it comes to the harness, the benefit here is that if your cat is pulling, it is attached to a harness, so the weight and the pressure is distributed across the chest it would not cause that potential injury to the neck.
The minus point here is that the harness is not likely to discourage the cat from continuing to pull because it does not render the feeling of discomfort for your cat if it keeps on pulling. However, now some harnesses are specifically designed to help with that.
There are certain harnesses that clip in the front rather than over the back, so when the cat pulls, this type of harness tends to squeeze its shoulder a little it and pull the cat off the side and make it deviated off in a direction they do not want to go.
And gradually, the cat will learn that it should not pull and gives up this bad habit. In short, the collar or the harness has its own pros and cons and you should consider those before deciding between them.