This is an awkward question, because food is about so much more than chemical interplay on the tongue, and how molecules decay over time. If all we cared about was getting proper nutrition, we would swallow a handful of pills each day which contained the nutrients we need, washed down with a shake containing bulkier elements like proteins and carbs. If all we cared about was taste, we would construct artificial foods with perfectly synthesized flavor profiles. (I'm guessing we'd wrap our perfect mix of nutrients into beverages, if flavor was the goal. After all, we already do have a host of artificial flavored sodas and such out there.)
But food is about so much more than that. Presentation makes food look engaging. Textures and smells have a huge impact on whether you find a food enjoyable. Wine glasses clink (particularly when toasting) to engage your hearing. The ceremony around uncorking a bottle creates a definite atmosphere which will color your perception of a meal, even down to how dishes taste. So, as easy as it may be to find links to articles about bottle seals and preventing air exchange, that is by no means the sum of the flavor in a bottle of wine. And anyone with experience of different dining environments, who enjoys uncorking a bottle, will find much changed in the flavor by the change from a cork to a screw-top. Yes, it's psychological. But really "flavor" is about how chemical impulses from your senses are interpreted by the brain; all flavor is psychological. And all of your senses work together; it's never about a simple signal from one sense.
Now, all that said, if you are NOT steeped in wine tradition, you likely will enjoy a glass of wine from a screw-top bottle perfectly fine. The fluid will be preserved at least as well, and if the only thing which changed in your meal was the un-corking became an un-screwing, a non-connoisseur probably wouldn't even notice. (Except all your "wine snob" friends will have a new topic for the next 20 minutes.) In wines produced to be consumed within 5-10 years, I highly doubt there is any worthwhile difference between any sealing method. And I doubt any of the wine collectors have allowed screw-top bottles into their collections yet, so we're still hundreds of years shy of long-term storage data.
I'll add that I had heard the common idea that cork is a depleting resource. This is often mentioned as a reason for the shift from corks to other closures in wine. I tried to Google this, and found several discussions (on semi-public forums, so I'll leave research to the reader rather than provide links) about this being a myth, and the shift being caused by a desire to prevent contaminants from getting into wine. So, it seems bottlers feel cork is a poor choice for wine.