1 and 2, are different games, in graphics, gameplay, style and as an overall concept, as well. 1 is a bit more "niche", with certain features, like getting blind drunk (nice effects) and it even being a mini-game, interesting mementos of intimate encounters (really liked those cards, especially the game extras calendar compiled by those), the group fighting style (really useful), the richer and more complex alchemy (including crafting your own Fisstech and even making use of it), special secondary weapon fatalities (hello, assassin dagger) and overworld utility (hello, torch), etc. The mini campaigns were also very okay.
2, on the other hand, feels more action packed, more console-ish, is a bit simplified of sorts, but brings new features in play, forces you to fight like a ninja (always rolling, evading, going sideways to avoid incoming blows) and is a different game, on many levels.
You can enjoy it perfectly fine, on its own. This was also a very old question, especially here.
* Do you miss much story-wise without playing the first game?
* Is the second game more enjoyable than the first one?
* Does the second game still have all that weird sex card nonsense or similar?
* Is the second game all-round less cringe-inducing?
* Are the quests less dull?
* Does the writing improve?
1. No, you don't miss much, besides dialogue gives you hints, at various points.
2. Depends. Even i who liked 1 more, i find 2 more enjoyable. This is the general going.
3. No, no cards. Instead, live cutscenes (i prefer the cards, though...)!
4. What do you mean "cringe" inducing? 1 was fine. It even had long philosophical debates, lol!
5. Depends. RPG quests are always boring and everything has been done before. I don't believe any The Witcher games' quests are boring.
6. The Witcher has always been praised, for its writing. Again, what do you mean "improve writing"?