I feel like I can clear some things up here.
Obito couldn't use his Kamui because he didn't have another dimension to exist in. I guess he could've gone to the real world but would risk getting hit by something (not even sure if Kamui can work like that).
Obito's Rinnegan was used for one purpose and that was for shared field of vision within the Reanimated Jinchuriki. Obito more than likely doesn't know how to use most Rinnegan techniques as he hasn't trained with it.
The only reasonable argument is the lack of Wood Release. He's used it before so why wouldn't he use it then?
Overall though, Kakashi isn't a terrible fighter. He's gonna toe to toe with some of the best and in this instance his taijutsu was just better than Obito's - it's always been better.
Though Kakashi didn't beat Kakuzu or Pain, Kakuzu had 5 lives and Pain was pretty overpowered, even to the point where Naruto didn't really beat him (Kyuubi went crazy, almost went 9 tails mode, Pain kinda had to stop that)