Sympathy is probably the wrong word, as I don't know that Truman Capote actually felt sorry for Perry Smith, but he did empathize with him. That is, both personally and in his writing, he could understand and tried to express what it was like for a person to be facing the death penalty.
The greater achievement of the book is getting the true story of what happened, but he also, for perhaps the first time in literature, put a human face on the condemned. He at least provoked some thought about the realities of capital punishment in a country that overwhelmingly supported the death penalty at the time.
One of the critiques that I had read years ago speculated that Capote was not trying as much to sympathize with Perry Smith but rather to demonstrate how a man could become the person who was capable of the act of murder at the level which Perry had committed. Capote had experienced his own rough and unusual childhood of unhappiness and this was one way in which he could relate and empathise with Perry. The time he spent getting to know him and learning more about Perry had created a bond.
Capote was able to identify that even men who walk the last mile to their execution have fears and a degree of humanity. He wanted this part of Perry to be portrayed. He wanted to humanize the man who had become a monster to the media. Initially, he wanted to write a story, but the time and events that followed during their interview time led to his developing an understanding that a human, even the ones capable of murder, have feelings and wounds.