New Running Shoes are almost exactly like Old Running Shoes, except they are slightly better. Grants a 75% movement speed boost when worn. The boots last for approximately 3000 blocks before turning back into Old Running Shoes (Old running shoes give a 50% boost).
Enchanting the boots with unbreaking doesn't seem to have any effect, but at the moment they should break, the damage bar resets. (this could also have been caused by sneaking at the exact moment they broke, but I am not sure). After this, if the player receives damage (not from falling), the new running shoes break and DO NOT revert back to old running shoes.