In the big climax at the end of the crossover, Barry was able to defeat Thawne.
Ultimately, however, Barry couldn’t bring himself to kill Thawne, and he literally let his arch-nemesis walk away without even trying to capture and imprison him.
Thawne is free to cause even more trouble for everybody in the Arrow-verse, and Barry may come to regret letting him go.
No, Eobard Thawne returned to mess things up yet again in Central City, once more in the form of Harrison Wells.