Smart pots and air pots, almost the same thing, they both have their merits
smart pots are easier to water, less messy, I find water pours out of the holes in the sides quite ridiculously sometimes from air pots, but air pots are easier to take the plant out, transplant etc (just undo the tags and unroll the air pots) or just plant small pots in big ones without removing them, once the roots aren't in contact with air, they'll just grow through the side into the next one (but you may be able to do that with smart pots too not sure what sizes they come in).
They both give significant improvements over normal pots as the root structure is just ridiculous, more surface area, better nutrient uptake, more oxygen etc = better/healthier growth, you can also fit a much larger plant in a small pot, I've done a full grow in a 4.5 litre air pot vegging for 5 weeks, and they were fine, just needed watering quite often when they got big.
As for oxygen, they get more because the roots have a larger surface area, you can't really over water because, unlike normal round or square pots, any excess water seeps out of the sides and evaporates or goes into the drip tray so the soil doesn't get waterlogged really.