They're pretty close. Stamkos from '09-10 to '13 led the league in goals and points, was 1st in GPG and 3rd in PPG after Crosby and Malkin, was a Hart runner up, 2 time Richard winner, and had point finishes of 2nd, 2nd, 5th and 5th and PPG finishes of 3rd, 3rd, 6th and 7th.
Kane from '13 to '16-'17 was 2nd in points to Crosby, tied for 3rd in goals with Crosby and behind Ovechkin and Pavelski, 3rd in GPG behind Ovechkin and Stamkos and 3rd in PPG behind Crosby and McDavid. He won the Art Ross, Hart, Pearson and Smythe, finished 1st, 2nd and 5th in points and 1st, 4th, 4th and 5th in PPG.
Stamkos was healthier and the better goalscorer, but Kane had less help and was the better play driver. Stamkos was better defensively and a center, but not a notable defensive player and if anything Kane brought more of a centers game to the offense. Kane's peak season was probably better, dominating the Art Ross race, but 60 goals is arguably more impressive historically.
I might give Stamkos the slight edge in the regular season in terms of impact, simply for health, but overall I think they were a wash per game. The separator is the playoffs, where Kane has been one of the best performers of this era, sitting 3rd in points, 5th in goals and 6th in PPG among those with at least 50 games, while Stamkos has largely been a disappointment with only 35 points in 49 games.