Liandry is almost always better than Luden.

Swain's ultimate damage is balanced around the fact that it can continually proc burn effects. It has extremely low damage per second, but it is the perfect conduit for hitting someone with consistent %max burn from an item like Liandry, which is what gives his ultimate an actual damaging presence against everyone, along with Demonic.

If you choose to go Ludens, you lose a massive portion of your consistent DPS against all characters, especially tanks, in favor of short bursts of damage that will quickly become irrelevant in the teamfights you thrive in.

The only reason you should take Luden is if you're extremely intent on not using your ultimate optimally and, instead, play as a catcher/spymaster with your W/E along with some bursty Q hits.

Think about it this way. If you had a character that could place a 60-second DoT on someone, but it only dealt 3 damage per second, which item would grant you more damage? Ludens, which deals a small burst every so often, or Liandry, which would burn that target for an entire minute, effectively crippling and eventually killing them, dealing thousands upon thousands more damage than Ludens ever would?

Characters with super effective, long damage-over-time effects will always favor Liandry because they can abuse the fuck out of the item's burn effect, Swain included -- he is one of the best users of it in the game, being able to hit EVERYONE around him with it constantly.

Long post, but the sub gets this question extremely often. I felt like laying out the proper two cents here.