As an American, I have more knowledge of the business side of the US sports, so forgive me if I mistake or misunderstand how the finances for a Premier League club work, but my understanding is that there are substantial revenue differences between Premier League clubs that, like an MLB team, can be used to a competitive advantage (if used smartly). This link, for example, has Chelsea at €513 million in revenue for 2018-19 season, while a club like West Ham had €216 million in revenue for the same year: https://soccer.nbcsports.com/2020/01/15/where-do-premier-league-clubs-rank-on-rich-list/
To me that looks somewhat similar to the gap between the Dodgers' and, say, the Padres’ respective revenue streams, and while the MLB financial structure has disincentives for spending above a certain amount, a motived owner can pay the luxury tax to do so, if they think doing so will enable them to win.
For example, John Henry wouldn’t go into the luxury tax to retain star player Mookie Betts, who had recently won the MVP and led the Red Sox to a World Series victory. The Dodgers were willing to go into the luxury tax, so they traded for Betts, gave him a highly lucrative new deal, and subsequently won the World Series. Now, John Henry could have paid to keep Betts, the Red Sox make enough revenue to do so, but he didn’t want to spend into the luxury tax (there are other non-monetary penalties for reaching or staying in the luxury tax, such as loss of draft picks, it should be noted).
On the other hand, NFL teams are constrained from exceeding a hard cap and cannot utilize a revenue disparity in the same way. If a team is willing to pay more for a star player, it is about how much of the set salary cap amount they are willing to allocate to that player, not about how much of the team’s revenue that the owner is willing to pay to the player.
The systems are all very different from each other, but both the Premiere League and the MLB, to my understanding, present an opportunity to outspent the opposition in a way the NFL does not.