That's an interesting way to look at it. Barnes was the more impactful, important (not insulting baseball but it is what is) hire.
In terms of just on-field performance though, it is Vitello, and honestly I don't think it's all that close.
TV has won 2 regular season titles and 2 conference tournaments. In basketball terms, he's had 3 #1 seeds (including 2 #1 overall seeds), (at least) two Elite Eights, and 4 Sweet 16s. Doing it in far and away the best conference in the country, and he inherited a program that had been dead in the water for longer than basketball had. It would have been really easy for TV to have improved the program, but have trouble getting over the hump due to the SEC's depth in baseball, but he's already been the best team in the conference multiple seasons.
Barnes has 2 regular season titles, 1 conference tournament title, no 1 seeds, 1 Elite Eight, and 3 Sweet 16s. And he's been here for 2 years longer than TV. And while the SEC has gotten much better in basketball over the last 10-15 years it isn't far and away the best basketball conference. Rick has been awesome, but honestly Vitello's run in baseball, purely in terms of on-field achievements, is even more impressive.