This article is from 2011, but today on Spotify Eminem still has more monthly listeners than Kanye West (53M vs 51M). Eminem also has several songs that have over a billion streams (one with >1.5b), while Kanye has just one and it's at exactly 1b.
This discounts Kanye's production work as well and might discount many of his collaborations, but I expect Eminem to still have more listens on spotify.
However, in terms of influence on hip hop and pop music as a whole, I think Kanye is above Eminem and it's probably not close. Unfortunately, that's a lot harder to measure.
If we're talking overall influence, it's Dr. Dre and then everyone else can get far back in line.
Kanye likes to claim that his music wasn't about gangster rap and that's why he was sidelined for... a couple years... meanwhile, Dre not only made NWA and Snoop Dogg but managed to convince the entire rap world that a poor white kid with drug problems and abuse issues was the next huge thing by doing things that nobody had ever thought to do before.
Kanye’s 808 & Heartbreaks has been claimed by many rappers from the 2010’s and onwards to have been a major influence. He really went all in on autotune and introspective lyrics. I much prefer Dre but his influence is waning.
The specific claim was "the most popular rapper/hip hop artist of all time". For that claim, I don't see a good reason why the last decade should weigh more heavily than the decades before.
The first time I remember hearing about Kanye was on Jay-Z's Black Album, "Kanyeezy you do it again, you a genius", the criticism lobbed against him in the early aughts was that he was a brilliant producer, but not a rapper, and then College Dropout came out, and changed that. It's really a shame to see all of this, Kanye is one of my favorite musicians of all time.
This is a very dry comparison between the two, as it only looks at numbers. Is Nickelback has far better commercial success than Rage against the Machine, but I don't think most people would rate Nickelback higher than RATM. Stronger may be Kanye's best selling track, but it's his easily least influential.
Slim Shady stands up [0].
[0] - https://iamyourtargetdemographic.com/2011/08/30/kanye-west-v...