This post describes the difference between the relationship systems in Love/Hate and the Dialogue System for Unity, especially regarding interactive conversations.
The Dialogue System has a simple relationship system in which you can manually adjust relationship values between characters, typically as a result of the player's conversation choices. (More info: Manual, Relationship Functions)
Love/Hate does not do branching conversations, but it can integrate with the Dialogue System for branching conversations. Love/Hate's relationship system is more sophisticated. In Love/Hate, games can not only adjust relationship values as a result of the player's conversation's choices, but they can also automatically adjust relationship values as a result of regular gameplay actions.
Love/Hate was inspired by something that bothered me about Mass Effect 1 (which is otherwise one of my top games of all time). Mass Effect 1 has a hard-coded event on one planet: If you run over too many space monkeys with your Mako on one specific planet, a companion NPC will get upset. But, since this is hard-coded, if you run over space monkeys on any other planet the companion NPC will not take notice. This is because the event was specially hard-coded by the writer. In Love/Hate, you can define information about regular gameplay actions, and nearby characters will automatically judge those actions when the player performs them. This way you don't have to hard-code specific events in specific game locations. (More info: Manual, Video Tutorials)
If your game doesn't need that level of detail, then you can get by with just the Dialogue System. If you do want that level of detail, get both assets and use the free Dialogue System integration included in Love/Hate.