Even though I like Minato because oh well, he's Minato, Sasori to me at least is a far more interesting character.
His character is really tragic and he stands on a very morally-gray area and this is what I liked most about him. This was, imo, the golden era of Kishi's writing before it all turned into a power-up fiesta.
There a "funny" part in this whole thing.
I have wrote a lot about the whole shinobi=tools thing when analyzing Sakura and one of the best depictions in the manga I think it’s Sakura’s and Sasori’s battle. I think that Sasori and Sakura are like Yin and Yang from this point of view.
I always saw him as the puppet, but not in the sense of literally puppet like he was, but in the sense of being a puppet of the system that governed the Ninja countries at that time. Ironic, if you think about it. The thing he ran the most from, being someone’s puppet, he already was before even knowing it,because he had given himself to a system that were controlling the human beings like puppets. On the other side, though he in a way, considered Sakura to be a puppet for having feelings [don’t know how to explain this right now as I am on the run but hope you get it], she was the one that was actually his total opposite. She studied all those sayings, shinobi code nr. 25 being the deepest reference to that, however, she didn’t fell under that system, she didn’t become a puppet of the system that governed those times, thus, in the end, she was the one who won, while Sasori lost.
People always said that Sasori killed himself or that he let Chiyo and Sakura win. While it somewhat would hold a truth, I find it not totally true.
For the very first time in a long time, Sasori falls prey to human emotions and he gives in recklessly, that's why Chiyo managed to land the final hit. Chiyo and Sakura remembered him too much about what it meant to be human, what it meant and how it felt to miss his mom and dad. These were the very reasons he turned himself into a human puppet because he wanted to throw away his human emotions and care about nothing but his undying art.
Mother and Father were his very first puppets as humans and they were made because he wanted so much to have his parents along, he kept lying to himself that this way he'd have them but when he realized that he couldn't bring them back, he decided to kill "his heart".
That's why at the end he rushes to kill Chiyo after impaling Sakura, because they remembered him what is like to be a human so he wanted to kill that last trace of humanity represented by the two. But because by that time he already had given to his human emotions, he recklessly got killed. Symbolically in his mother and father's arms.
Anyway, I won't go further with rambling but yeah, between these 2, I prefer Sasori. He has much more depth than Minato, imo, though Minato has some depth of his own. But not to the extent Sasori has.