I don't think its really been shown at all - this answer on Quora seems pretty balanced: http://www.quora.com/Wine/Do-wines-with-screw-caps-age-as-we...

The effects of micro-oxidization are definitely not the only change in taste that happen to an aging wine.

It's a pretty major part though. The study that I remember reading was done in Australia with white wines that had been aged for 5 years with different closures(though in the same environment). The sensory results did indicate that the choice of closure did have a pretty significant impact in the way that the wine aged. Synthetics had more oxidized notes, Screw cap wines tended to be reduced and have varietal characteristics consistent with younger wines, while cork aged as expected.

"Better" is a subjective term, and most people would actually prefer the fruitiness of a youthful wine. Heck, I know I do most of the time :) But there's something that develops with certain wines over time that I'm not just convinced that you can get with screw caps.

True

Maybe it's even part of some wine/wood interaction

Screw caps may be ok but they certainly look cheap.

I'm not convinced low-end corks are better than synthetic cork (in the case of some aging), and maybe the technology improves, leaving the solid corks to the expensive wines.

Supermarkets in France sell corks, I remember seeing them split by aging time, from 1,2 years up to around 20 years