First of all, check out Pornography. That is by far the "darkest" and most depressing Cure album out there, and probably one of the darkest albums of the 80's in general. If you enjoy that, then you should go and check out Disintegration next. Disintegration is another really good album by The Cure. It was the album that made them big. It is a classic. The stuff done with keyboards on that album is still chilling... even to this day...
There are some similarities between Katatonia and The Cure (mainly a similarity between Jonas and Robert Smith's vocals!), but The Cure was one of those bands that inspired and influenced a whole bunch of people. Hell, The Cure has always had the taboo of being the all defining "Goth band," even though they honestly played a variety of different styles including radio friendly pop music during their "long" career.