I've played through half of NWN2 a few years ago before my graphic card died and I had to take a long break from the game. Now that I'd be able to continue, I don't really feel like loading the old savegames, but I don't want to replay everything I know already either. I'd prefer to start something different for now.

So I wonder, do I miss out on something if I play Mask of the Betrayer without finishing the official campaign first? Are they somehow connected, storywise? Am I expected to play it with a high level character or does it start from scratch again?

It does continue the story line to a degree, but you will know just as much of what's going on if you start with a new character. Your Character will be levelled up at the start, & your carried through character gets to keep very little of his/her previous gear.
So just start a new game if you like.

Mask of the Betrayer begins right after Neverwinter Nights 2 OC ends, and you play the same character (having presumably completed the "good" ending of the first game). If you create a new character, you will automatically be boosted to level 18 and given appropriate equipment. However, the plot is completely unrelated to the first game and very few characters make a reappearance, so you don't need to complete the OC to enjoy MotB.

The MotB plot is quite separate, but will contain some (NPC-related) spoilers for the OC and it culminates in revisiting several OC areas, so it will make far less sense if you haven't played the OC.

I would really recommend playing the OC first, especially since there is enough flexibility in character creation to make a new game (with a different class) a fresh experience. If you didn't like the OC for some reason, it's likely those reasons would apply to MotB as well.

Well, the thing is that I still see RPGs mostly as story-telling games and not so much as action or strategy games, which makes the thought of replaying them and re-reading or clicking through all the dialogue quite unattractive to me, because the story aspects hardly ever change on a replay and if so, only minimally. I also have quite a good memory when it comes to stories, compared to other people who can e.g read a book twice within a few years and still enjoy the story as if it was the first time because they've already forgotten most of it ...

I didn't dislike the OC, I thought it was okay, in any case a lot better than the OC of the first NWN. I especially liked the companions and the interactions with and between them, and I liked that it featured githyanki. But the plot wasn't all that gripping in general, not to the extent that I'm curious how the story will evolve. And I have to admit I wasn't that fond of the graphics, GUI and camera changes compared to NWN. Not that NWN has better graphics but somehow they feel more natural to me. But I've often heard praise for MotB and I think I also read that it is somehow related or similar to Planescape, a setting and a game of which I am a huge fan.

Maybe there's a third alternative for me, and that would be playing a community module first, to get accustomed to the game's look and mechanics again (possibly in preparation for continuing the OC), while experiencing a new story at the same time. And if it's anything like the first NWN, there should be community modules that are even better than the official campaigns?

There are some excellent community modules. I think your idea of trying one out to get a feel for the game again is a great idea. As far as the transition from NWN2 to MotB goes, you can easily start up a new character without really missing out on anything important from the first game. While it is a continuation, it's done in such a way that you can dive right in without ever having played the first campaign and not be handicapped. Probably the biggest thing you'll miss out on is a couple character levels at the start (your character can reach level 20 at the end of NWN2, while if you start a new character in MotB, you'll start at level 18).

You can import your character. The story and quests make absolutely no sense to me. Why it's regarded as better than the original game is beyond me.

The D&D games make a fair load of assumptions on the player's part, so that's hardly surprising - even NWN2 assumes that you have at least a basic understanding of the D&D universe, and even the pen-and-paper RPG at times. If you don't, well, tough.

Since the main campaign begins at level 1, it throws all manners of kitten-saving basic quests at you. It may get quite confusing towards the end if you don't know anything about D&D; since MotB starts at level 18 and ends somewhere beyond 30, which is roughly equivalent of being a demigod, the themes are deeper in the Forgotten Realms setting.

What exactly are your problems with it?

The problem is that it's non-linear, and a great deal of the plot can be missed if you're not careful. Even then it works on implication and suggestion as much as simply telling you what's going on. Taking the time to read some of the in game books can help, particularly Lamentations of the Dead, and talking with your companions and certain NPCs can be equally revealing.

However, if you can keep track of what's going on, which can be difficult at times, then MotB tells a deep, multilayered story based around a number of central themes, including, unsurprisingly, masks (in a philosophical, rather than literal sense) and betrayal. Other major themes include love, faith, and duty. This story puts the, "Go places, kill things, save the world" plot of the OC to shame.

Of course, if all you're looking for in a game is "Go places, kill things, save the world" then the OC and SoZ are probably what you're going to prefer, especially since they have a sense of humor about themselves.