I suspect Jesse's might come sooner, she already had a shot of speed and is a recurring who can run back to Earth-2 at the end of the season.
Yea, the chances of hers appearing sooner are better compared to Wally's. Wally's would probably be a cliffhanger or near the beginning of season 3.
One or both of them will be in a coma with one having a speedy recovery due to speed force and the other barely recovering. Jesse awakes, speeds away without knowing it, confused, calls Dad, they run tests on her, confirmed speedster.
Wally stays in a coma, Joe by his side, Joe rambles on about family stuff, Joe's holding Wally's hand, Wally's hand moves and grips Joe's hand, the camera zooms up to Wally's eyes and we are left with the speed force running through his eyes.
Getting rid of Zoom, Jesse is now her Earth's 2nd Flash. Jay returns to his Earth after the reveal. Barry returns and is now a better speed force user, with his new found ways in using the speed force he gives some speed force to Jay. Jay trains Jesse along with Wells. Barry trains Wally. Season 3 will focus on Grodd attacking both Earths by sending his army to attack the speedster family.