Collars and harness are a big topic amongst dog owners
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Without trying to sound like Boris I tend to stick to the science.
Before going any further the damage by collars and harness is always done by the dog pulling not just wearing them (apart from shoulder harnesses which are the work of the devil!)
There are many scientific studies to show that collars do damage to the Trachea, Larynx, Oesophagus, epiglottis, lymph glands, thryoid if a dog is allowed to pull on the lead attached to a collar. Tracheal collapse is also thought to occur with a tight collar on the neck. Also interestingly there is some damage to a dogs eyes from pulling on a collar for a long period of time.
So that does then to imply that a harness is better but tbh there have been less studies on a harness.
What has been studied is cross the shoulder harness can causes growth issues in puppies and dogs so I would avoid them.
The Y harnesses sound like the perfect answer then! However what has been studied is that a dog that pully in a y fronted harness tends to put more weight on the off side leg to the owner.
On a personal level I will always use Y fronted harnesses on my dogs and ensure that they are trained to walk without pulling.
If you want to read the papers
Grainger, J., Wills, A. and Montrose, V. (2016). The behavioral effects of walking on a collar and harness in domestic dogs (Canis familiaris). Journal of Veterinary Behavior, 14, pp.60-64.
Also been one more recently by Zilch on harnesses