I would say there are differences between neutral and new barrels. It turns out there is quite a bit of oxygen contained in new wood, so a neutral barrel that just had wine removed and a new batch put in doesn't provide the same oxygenation. As Glowin indicated, you still get the oxygen that passes through the wood or between staves, but the oxygen contained in the wood is partially depleted. The addition of new oak cubes not only provides flavor, but also provides the needed oxygen. Some young heavy tannic red wines, particularly mountain fruit, require significant oxygen in the first few months or they may become reductive. I've found that 5 staves (36"x2.5"x.375") are needed for a 30 gallon flextank which is supposed to be oxygen permeable like a 2nd year barrel. Without the staves the wine will go reductive quickly. You can add oxygen any way you like, racking or oak etc., but judgment is needed as lighter style reds don't require as much.