The rubber in a 20 year old tire will be hard and lack good traction regardless of how much thread is on it. Replace both.
1/8" was added to each side of the tire In other words, nothing much was gained or lost. It was probably a matter of not being able to find a 2-3/4" tire but a 3" tire was available.what was gained or lost by going away from the 2.75" to the 3.00" ?