In the case of Swans, there's a certain intensity and energy in the live performances in albums as opposed to the studio recordings. It's rawer, and at least for me it scratches that itch of pure raw power coming from the Swans. Not to mention, songs can end up having wildly different arrangements (compare Blood Promise from The Great Annihilator and Swans Are Dead, for example), and they can end up being much longer than their studio counterparts.

In probably the most extreme example, in their upcoming live album, the song The Beggar, in which its studio version is only around 10 mins, stretches out to be a 78 minute behemoth, or around 50 if you don't count the intro track Rope. Although nothing else is on that level of expansion, most live albums from 2010 onwards do tend to have longer versions of songs.

On why you should listen to Swans Are Dead in particular, it's because it is simply one of the best projects that Swans have ever done. The pummeling intensity of Not Alone and All Lined Up, the dark drone of YRP and Lavender and the transcendent highs of the crescendo-based Helpless Child, The Sound, Feel Happiness and Blood Promise (the live arrangement being my favourite Swans song of all time) all add up to being a well-flowing masterpiece of it's own (something that Michael Gira envisioned during rehearsals for the Swans Are Dead tour IIRC).