What is the difference between Civilization V: Game of the Year Edition and Civilization V: Gold Edition
Solution 1:
From Wikipedia:
A Game of the Year edition was released on September 27, 2011. It includes all four of the "Cradle of Civilization" map packs, the "Explorers Map Pack", as well as most of the new civilizations (Babylon, Spain, Inca, Polynesia, Mongolia, and Denmark), their respective scenarios, and the official digital soundtrack. However, "Civilization and Scenario Pack: Korea" and "Wonders of the Ancient World Scenario Pack" are not included.[47]
A Gold edition was released on February 12, 2013. It includes all "Cradle of Civilization" map packs, the "Explorers Map Pack", the "Wonders of the Ancient World Scenario Pack", all the DLC civilizations and the Gods and Kings expansion pack.[48]
So the Gold edition contains all of the GOTY content, plus the Korea and Ancient Wonders DLC packs and the first expansion Gods & Kings. G&K is the most significant difference between the two editions because it's a full expansion that adds a lot of new mechanics and content to the base game: religions, espionage, new techs, improved combat and diplomacy, plus several more civs and city-states.
Most of the DLC packs on the other hand are extra maps and civs that just give you new options to choose from, but as someone pointed out they are often required to join online games. They are not strictly necessary, especially for single player, but they do offer more variety.
I disagree with the other answer's conclusion; G&K is a massive upgrade that is well worth buying Gold over GOTY.
To address your edit, Gold edition does not include future DLC: there is now a second (and very significant) expansion Brave New World which is not included in either of these editions. To get the full package you would need to have Gold + BNW, or at least Civ5 + G&K + BNW.
Update: The Complete edition has since been released, containing "both expansions and all the DLC packs."
Solution 2:
The major differences are that Civilization V: Gold edition includes the Wonders of the Ancient World Scenario Pack, the Gods & Kings Expansion Pack, and the Civilization and Scenario Pack: Korea. Civilization V: Game of the Year edition does not.
Below is a comprehensive list of everything included in Civilization V: Gold edition;
By getting the Game of the Year edition you're not missing anything that is required to play the game. The content that you are missing mainly comprises of additional maps, a few more scenarios, and civilizations.
IMHO, the game is immerse and lengthy enough to be content with GOTY edition. If you ever wanted those missing expansions, you can always purchase the Gold Upgrade from Steam or the expansion packs later.