Oxygen permeability is potentially an issue. In primary, not so much as the yeast is utilizing oxygen in the lag phase, you generally aren't in primary for long, and there is a lot of CO2 being produced that purges the headspace. Buckets are great primaries as they are easy to clean, especially since you will have the most trub/lees in primary.
If you want to age in bulk, getting off the lees and into less oxygen permeable glass makes sense. You also want to minimize the surface area of liquid and the volume of the headspace to further minimize gas absorbtion, so a container with a neck is particularly useful for extended aging.
That is why it is so important to use a carboy appropriate for the size of your brew - if you are brewing 3 gallons and rack into a 5 or 6 gallon carboy, you have massive amounts of headspace and the surface area of the liquid is as large as it can be. These are both factors that maximize the potential for oxidation and infection.