Analysis
Itachi vs Sasori
Sasori is literally the worse possible match for Itachi for 2 main reasons: his strengths are itachi's weaknesses. Itachi in his sick state would pose little match for Sasori.
As narutopedia states, Itachi's weakness is fighting prolonged matches against strong opponents. Since he can't do this, he resorts to strong genjutsu's to end a match quickly.
Sasori, as a puppet, has literally infinite stamina. Thus he can control the pace of the battle and outlast most opponents. He can prolong a match against sick itachi, until overuse of MS, or low stamina makes him succumb to his sickness, or until he simply passes out.
Itachi would have to resort to strong genjutsu's to end the match quickly, but this is a problem.
3 things almost everyone (including sasori fans) ignore when talking about him in vs. threads
1. Genjutsu's don't work on him. This has been long debated, but simply using the facts from the manga/anime, the fact is that he only has a heart. The real sasori is his heart. He doesn't have a brain IN his heart, like some say, because it is stated that he only has a heart/is a heart, not has his lungs, brain, spleen, stomach, liver, kidneys, etc. in his heart container. Without a brain, no genjutsu can work, since genjutsu's are illusionary images that use the physical brain of an opponent. Sasori also doesn’t have a normal Chakra circulation System (CCS). He only has a heart that projects chakra threads through his fingers, or from a right cavity. A genjutsu would paralyze his body via his chakra that runs through his body, but with a puppet body (no CCS), his body would not be paralyzed. Basically, only the chakra in his heart would be distorted, but w/o a brain, no genjutsu would actually do anything. For those who know of ghost in the shell, consider cyberbrains- not physical brains you, but they are cybernetic computer brains. That which would work on a normal brain would not work on such a computer brain, thus to say genjutsu's work on a puppet is like saying one would work on a robot. Now this is not to insult readers, because I admit that it makes no sense. Sasori can stand in a cloud of gas and not die, since he doesn't breath. But w/o oxygen, how does his heart cells not die- w/o lungs, how is his heart sustained? He shouldn't be able to live. Same w/thinking w/o a brain- it doesn't make sense, but going strictly on the manga/anime that says that he only has a brain, I must say that he somehow thinks w/o a brain. Kishi perhaps needs a lesson in biology (or he should have explained Sasori's biological makeup), but the fact remains that people should take that up with him. My stance is that genjutsu's thus don't work on a puppet.
2. Everyone acts like the second Itachi pulls out susanoo, that it would be over for Sasori. Not so- poison gas & poison from smoke bombs CAN go through susanoo. This should be obvious- susanoo is only a chakra form, which is energy. Gas can go through it as it isn't solid. Air/gas has to pass through susanoo or else Itachi would suffocate. It isn't sealed. When Mei faces Sasuke, though his susanoo is incomplete, her acidic mist (gas) slips right pass the chakra of susanno and melts it's ribs. So yes, poison gas can go through susanoo. Everyone also forgets that Sasori has 2 rotary wind blades on either side of him, allowing him to fly. Thus he can easily fly outside of the range of Susanoo's sword, while dropping endless poison gas bombs on Itachi, until the entire battlefield is gassed. Some say itachi can hold his breath. It is implied that Itachi had TB, as he coughed up blood in his match against sasuke. TB=respiratory illness. He wouldn't be able to hold his breath for long. Some say he could do what Sakura did. Yet Chiyo said it was reckless- it's a miracle Sakura survived. Yet even though she did, she was unconscious after using an exploding tag. Chiyo had to nurse her back to consciousness- who would nurse itachi back to consciousness? And the second he went out of it, Susanoo would disperse
3. Everyone jumps on the Amaterasu bandwagon, yet this might be the worse possible thing Itachi could do. First, Iron sand can easily block ammy. Sasori can switch his heart into another puppet case in a split second, before Ammy burns the puppet completely. He could then attach puppet strings to the former Sasori (empty shell now ignited) and send it towards Itachi. Contrary to what many say, Ammy doesn't burn 'as hot as the sun,' i.e. burn anything to ashes automatically, as can be seen with the Samurai armor in the Land of Iron, and the Raikage's arm. Only if Itachi constantly focuses on an object will it burn quickly. With sasuke, sasuke himself was caught on fire then shed his skin, which is why it burned so quickly- the trees around the Uchiha hideout were caught on fire yet burned slowly- not even 1 tree burned down. And no, a sharingan cannot automatically locate Sasori's heart, since it's NOT the Byakugan (might be wrong here). So sasori wouldn't just burn to ashes quickly. Even more, imagine 100 puppets, all caught on black flames & with poison weapons, flying at you at once! If Itachi used ammy against the 100 puppets, then he might incinerate some of them, but would only ignite most of them- Sasori's 100 puppet jutsu would be 100x deadlier! Itachi would inevitably be caught on fire by his own flames (everyone forgets that the user of ammy is not immune to his own black flames). I assume that Itachi can put out his own flames (despite the fact that narutopedia says only sasuke can), but he would have to concentrate on putting out the flames engulfing him while not being re-ignited by more puppets flying at him. So he would probably be re-ignited by black flames. And during this time of he'd have to not be so much as scratched by 1 poison weapon. He'd have to resort to Susanoo to defend himself, which requires great strain. Ammy also can't burn chakra/chakra strings like some say (I don't think so, but like many things here, I could be wrong. Btw, this is my first post, so go easy on me. I'm humble enough to admit when i'm wrong
Even more, ,with Sasori flying with his wind blades, Itachi couldn't hit him if he flies high and is dropping poison gas bombs. It's like trying to hit a fly with a gun.
Itach's fire element jutsu's are mid-range. Not getting hit with poison needles is hard at close range while doing a jutsu (itachi couldn't dog 2 shuriken at mid range while about to do a jutsu), and IF sasori gets on fire, then he can switch bodies and send the ignited puppet at Itachi, or put the fire out with a water scroll jutsu.
Some say Itachi could just make shadow clones and sit back and study Sasori's movements- Sasori could also make sand clones and study Itahci's movements- both have a 5 rating of intelligence in the Naruto STATbook. Sasori is said to be slow by many, yet he has a 4.5 rating of speed in the stat book- faster than Kakuzu, as fast as Sasuke and Kakashi, and almost as fast as Itachi himself.
Even more, with Sasori in Hiruko, Itachi might try to use that MS genjutsu on Sasori, and thus would waste chakra before realizing that Sasori was a puppet that couldn't fall for genjutsu.
When one adds all of this together, one can see that Itachi in his sick state would not win against sasori- sasori, once again,, would be able to strike Itachi's Achilles heel. The stamina factor alone is Itachi's weakness against Sasori, such that Sasori would be able to control the match and use poison to win with relative ease. I'm neither a Sasori fan or an Itachi fan, so I readily admit that Itachi would probably win in his prime (not going blind, and not sick). Fan=fanatic, btw, and I'm not a fanatic of any character. I just think itachi is overrated and Sasori is underrated.