Matsumoto should win this fight. Rukia is very powerful for an unseated Shinigami, but she's at a very low lieutenant level at her highest. Matsumoto is one of the more powerful lieutenants when she puts her mind to it. Also she's shown the ability to use her Shikai for physical defense so when her blade dissolves she can still block Rukia's sword and dodge all of her ice attacks.
"@BardofWonder said:"She beat the 9th Espada through luck and the Espada's arrogance. It's not like she overpowered Aaroniero. "true "
she was hanging with him in his normal form, & resoucefulness can come into play in a battle as well. Rukia's signature attacks are bettter & would certainly be able to kill her.