Why? This is out of curiosity more than anything, I personally think Kitsuchi wins too.
With what difficulty? I say Kitsuchi wins with mid-high difficulty.
My lack of understanding manga panels is what made me think Temari could cut her way out of the sandwich trap. I later on watched the anime and realized that it is way too thick for her to do so. Even if she could, the attack is fast and I doubt she would be fast enough to cut it completely. Even if she somehow miraculously managed to do so, she would still probably not be able to get away from the second wall. Unless of course she can fire a bust of wind at the ground to jump/fly away but she has never done this so it is mere speculation on my part.
Anyway most of the people rooting for Temari in this match up probably don't even know much about Kitsuchi as he is a relatively new character. Not only that, I doubt he has a fan base to support him either. If we use valid speculation, it is very likely that Kitsuchi can use giant earth walls, earth rock bullets, hiding underground and earth clones as well as his already mildly robust arsenal. With all of that, he can survive Temari's powerful wind attacks even if they tear away at his defences. Hiding underground is a common earth technique and while Kitsuchi is hiding behind a wall of earth, he can easily go underground and Temari won't know what happened. Later on he can appear behind her and punch her with a giant rock fist. Temari should have the reflexes to be able to defend herself with her fan but she will be sent flying and won't be able to fight any longer after that.
Also as a master of earth techniques, Kitsuchi should have the ability to create underground tremors which would destabilize Temari's footing. She could easily use her fan to balance her footing, however, this momentarily takes away her ability to attack giving Kitsuchi and ample opportunity to go on the offensive.
As for other factors in this fight, I think it should be obvious that Kitsuchi is more physically stronger than Temari as well as faster when it comes to foot speed and much better in CQC. He probably has a higher amount of stamina as well as he looks like a robust man. Temari is probably more intelligent as Kitsuchi seems more like a brawn over brain ninja and in part 1, Temari showed some impressive intelligent feats so I assume current Temari is a lot smarter.
Now what I said in the previous paragraphs makes it sound like a stomp match in favour of Kitsuchi but it clearly isn't. Temari's wind attacks can slice metal easily so I have no doubt that she can do the same with rocks. Still if Kitsuchi puts chakra into rock walls, they'll become even more durable. Also Kiri kiri mae is a very dangerous tech as it has the ability to completely change the terrain as well as use flying debris (tree and rocks) to decimate bury the oppoent. In part 1 as we all know, she effortlessly destroyed an entire forest worth of trees. During part 1, her wind did not have the power to slice metal and wood was the hardest solid structure that she could slice away. In Shippuden, she now has the ability to slice Samurai armour effortlessly with only her basic C ranked wind attack. We haven't even seen the extent of her jutsu power in Shippuden at all and I believe that her B and A ranked kamaitachi variants would do significantly more damage to the same forest where Temari fought Tayuya. She can probably slice buildings as well.
Now on to Kiri kiri mae... That jutsu was pretty OP for something a part 1 genin could use. It seemed more like a jounin level tech than a genin level tech. Before Naruto interfered with the fight against the 3rd Raikage, Temari commented that her only choice was to use kiri kiri mae. I don't believe it would have sliced the 3rd Raikage but it is clear to me that the power of that jutsu has increased tremendously.
The data book claimed that Katamari rides Temari's wind in order to use the momentum from Temari's wind to travel across the given area and slice everything in its path. Bare in mind that it is the weasel that does the damage, not the wind itself. Now I think Katamari is probably a lot stronger and the wind that it will ride will also be a lot faster, cover a wider range and will be overall more stronger. For this reason, I believe that her kiri kiri mae would be able to slice an even larger forest or maybe even a small portion of a mokuton forest.
Anyway that tech requires some time to prep as she has to bite her finger and pour blood onto her fan to execute it. For this reason, it isn't something she could use right away in a 1 VS 1 especially against an opponent of the same skill or even superior to her. Also Kitsuchi could still go underground to avoid the attack but all his clones and wooden defences will be completely destroyed. Still the debris created by the kiri kiri mae will probably help Temari more so than Kitsuchi as she'll be able to blow it away unlike Kitsuchi who will be forced to deal with it littering the battlefield.
