B/w Little Big Adventure and Another World. I like point and click style adventures like Broken Sword etc. I have never played these two before. Which should I go for?

Well neither of them are point and click but LBA is more of n adventure game i reakon

More of a hybrid, but it's hard not to recommend this: Quest for Glory.

EDIT: Not familiar with both games you mentioned, sorry.

Another World is a great game, but is more of a platformer, I'm afraid.

Sorry, I couldn't help with LBA, haven´t played it (this one isn't a Broken Sword alike game, neither).

Contrary to Broken Sword, both of these games are played with the keyboard, not the mouse, and they're based on good reactions. I think in Another World the controls are quite simple and intuitive, while the ones in LBA might require some time to get used to (you can switch between several modes, too: normal, sportive, aggressive and sneaky). In both games you can die a lot (at least I think you can - could be that in LBA you're just imprisoned if you fail, in any case it would result in having to do some things over again).

I haven't played much into Another World, but I suspect that there are no dialogues in it and that the story is told without words. In LBA you can talk to most other characters (unless they're hostile).

I assume Another World is mostly linear and I read that it's quite short, while LBA gives you more freedom on which places to visit and what to do first, and it's probably considerably longer.

LBA is more complex and has more similarities with traditional adventures, but it's more of an action adventure with platformer elements. Maybe a little like Zelda-type games, too?

Depends on what you're looking for and how open you are for trying new things (in case you want more games like Broken Sword, did you miss Syberia and The Longest Journey?). Anyway, I'd suggest watching some gameplay videos on youtube.

EDIT: Can anyone explain what savegame option they use? Does Another World even allow the game to be saved or do you have to play through it in one sitting?

I suggest you wait until tomorrow's sale and pick up Sanitarium if you are after an adventure game.

Otherwise, if you are flexible with your gaming choices, and determined to buy a game from today's sale then I'd recommend LBA. They are both good but LBA is more (slightly more) of a traditional adventure.

The answer is probably LBA. I love Another World, but it's quite linear and fairly short. The save system is based upon typing in the appropriate code. It's still a good game, great graphics for the time and good atmosphere, but it's probably not as good as LBA.