Wally has a joy to being a speedster that fuels him and makes him the best.
It’s well documented that Wally is the fastest, see below for another example. While Barry has seen a resurgence in recent years, and has been the flash chosen for recent media (Arrowverse, DCEU), he was first so that’s understandable. They brought him back in the comics around the time of blackest night with flash rebirth so 2009? He died in 86 with infinite crisis so for more than 2 decades Wally was the Flash for a lot of people. The justice league animated series (Timmverse) has Wally as the flash, and the heart of the justice league, which he was amazing in.
For many people Wally isn’t only The Flash, he’s an integral part of the Justice League, DC, and comics. During those years, his power was cemented and when Barry returned it was still established he was more powerful.
So while Wally has the power, and neither are really cutthroat fighters, it would come down to if Barry could be more creative than Wally to beat him, which I don’t think he is. Maybe if Iris and the twins were on the line, Barry would find it in him, but overall Wally.