I'd say bag in a box is probably less permeable to oxygen, but you need more equipment to fill them and I think you'd have a hard time connecting the taps to a piece of hose, as the taps will only open for as long as you have the button depressed. Polypin taps are a lever and you can leave the tap open for a whole session.
If you're a practical kind of person, you may be able to overcome the tap on a bag-in-a-box. Buy a box of wine. They hae the same size tap as the large ones used for cider.
As for polypins, you could buy a full one from a brewery and reuse it, or they're a tenner or so feom homebrew shops. Having given it some thought, you could use a cornelius keg to condition it and then rack it into a polypin, this would get around the permeability factor, but involves more cost and effort not to lose the C02 when racking.
This is the kind of thing you need to dispense with a hand pull from a polypin (you could use the same if you can find a way around the tap on a bag).
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