He didn't have an advantage against her they were equally advantaged. He could freeze her water but she could melt his ice. She may not have been serious the whole time but when Yamamoto cut down her fraccion she became serious. She attempted to take him down as quickly as possible so she could challenge Yamamoto, but she failed. Also it's not like Komamura fared well against Tosen. He only managed to break his arm. Tousen destroyed him and actually was killed by Hisagi blindsiding him.
Yes Toshiro would have lost to Luppi had the latter not been careless, but he did ultimately beat him. He was a mid rank Espada after all. He also struggled against Grimmjow's fraccion, but when you're using 1/5 of your power, I don't see how there's any shame in that. He beat him immediately after the limiter was released even though he was on the verge of defeat before. And as for Fraccion, Komamura himself went bankai and no limiter against a fraccion as well because the latter was stronger in base and release otherwise.
Soifon was losing to Baraggan, but of course she was losing. He's the ex King of all Hollows. Pre Hougyoku Aizen didnt even want to fight fairly and instead used his hax illusions to trick Baraggan. In the end Baraggan's own power needed to kill him. If Komamura had been the one fighting Baraggan it would have been even worse. But I can agree that she beats him primarily due to speed, but her shikai/bankai are excellent counters to his own as well.