He only kicked her because she thought Tatsumi would be frozen. Tatsumi is effective against Esdeath because he adapted to her, it would take awhile for him to adapt to Wave.
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Wave's Grand Chariot is more offensive as opposed to a more Tatsumi's defense oriented Incursio. Then there's this whole flight advantage to the former while the latter has invisibility. Tatsumi admitted that he would have been killed if it wasn't for blocking Grand Fall in his last skirmish; however, he wasn't aiming to fight Wave at the time.
In terms of power enhancements, GC is superior to IC. Plus, Wave has more experience using it; but this comparison went only as far as Incursio's "base form." Incursio V2 based on feats this chapter shows to be superior to Grand Chariot at the moment. I didn't seen much from Wave aside the skirmish that compares to Tatsumi, such as his speed and slicing Esdeath's ice clean. Until I see more of what my nig Wave, Tatsumi honestly takes this.
Btw, he was denting Esdeath a bit. But he wasn't really pushing her back as he also had Mine there as well. Then there was also Akame and Leone coming in to ambush. So as always, my Lady Esdeath still freezes. U_U