Not really. Champagne needs to have carbonation. Like your bottle of coke carbonation starts leaving the solution whenever it's opened. This proceeds within a closed of bottle, too (hence why the last glass of coke out of a bottle that's been sitting over a day is almost flat.

Both beverages do oxidize. The CO2 leeching from your champagne will protect it from most of the ill effects. However you can vacuumize your wine bottle, and due to it getting flat, this doesn't work with the champagne.

So technically your campagne doesn't oxidize, however it loses it's sparkle. With a champagne stopper you can mitigate this effect, just like you can mitigate oxidation by vacuum in a regular bottle.

Without these special stoppers you can keep both wines for three days, the white wine under the cork, the champagne resisting attempts to re cork, due to CO2 pressure.

They will both not be as good as unopened after the days. For different reasons.