Sony had its own sport simulations line at the time (NFL GameDay was a serious treat to Madden in 1997 and 1998*) so certainly isn't the presence of sport simulations in the first-party lineup the real reason of the rift between EA and Sega.
Simply EA has a history of bullying who is weaker than them both to exclude rivals from really compete with their sport games (by splashing more money for the licenses) and to trying to pilot platform holder to decisions who favor them (by leveraging their status as the biggest third-party publisher on the planet).
Sega by that time was a very weak platfom holder and I'm sure EA management thought it woud be easy to wrestle control from them.
In case it back fired they were sure Sega wouldn't be a serious contender to Sony and Nintendo for which they would still continue to produce games for.
EA already took Sega by the balls with the infamous Joe Montana Football deal and by forcing a better license deal to develop for the Mega Drive:
Sega approached Electronic Arts, developer of the Madden NFL series, and president Trip Hawkins, for help, suggesting that he cancel the upcoming Genesis version of Madden in order to work on the game. Hawkins agreed to help Sega but refused to cancel his company's game instead working on both projects. He intentionally made Montana a worse game than Madden, starting with the basic code for the former he removed the 3D field as well as cut down the number of plays from 113 to 100. According to Michael Knox a programmer on the game, most of the deliberate downgrading occurred after the company had already completed the game. Joe Montana Football missed the Christmas deadline and was released in January 1991, shortly after the Genesis version of John Madden Football.
I'm pretty sure there is some kind of undercover beef between EA and Nintendo since the early 3DS/WiiU days, the difference is that EA has no chance to bully Nintendo which is stronger than them.
NSW sales in US are trending toward it becoming the second best selling cosole in US history yet no Madden game has appeared on it lol.
EDIT:
* Top 20 best selling games in US for each year between 1995 and 2000 (source: NPD):
First-party published titles highlighted.