Corks or Screw Caps, Does it Make a Difference?
Short answer: not really.
The screw cap was invented and used to bottle wine as far back as the 1950's, but they were initially used to seal value-oriented jug wine. Boy have we come a long way since then. These days, you'll see screw caps used on a plethora of wines all around the world. The technology for screw caps has come a long way since the 50's, with a seal that is actually much more airtight than cork or even synthetic corks. Because the seal with screw caps lets in such little oxygen over the course of a sealed bottle's life, the wines used with screw caps can typically age much longer without changing the properties of the liquid inside. (Fun fact for those that don't know, corks allow air through the seal that ages the wine more quickly than a cap.)
In fact, you can find some outstanding wines with screw caps these days. Here are two of many I just pulled:
On the left, you have John Duval's Entity Shiraz. This 2012 Barossa Valley gem garnered 96pts in Decanter Magazine. And the drinking window for the '12 vintage is approaching (Current vintage is 2016) The Entity retails for $43.99. You can read more about it here
On the right, you have Ken Forrester's The FMC Chenin Blanc. This is the pinnacle of Chenin from South Africa, and won the Chenin Blanc trophy at International Wine & Spirits competition in 2015. The FMC retails for $69.99. You can read more about it here
Bottom line: wines that have screw caps are just as good as their corked competitors, and in some cases even better.
Oh yeah, did I mention you don't need a corkscrew?