So what's a bigger deal, winning the Premier League or winning the FA Cup?
MM and Navin are quite correct.
The league and FA Cup used to have roughly equal status; the league being the hard slog while the cup considered to be more glamourous / romantic. There used to be bifurcated European tournaments for to the winners too.
But with the formation of the Premier League, and the money fountain it engendered, the FA Cup slowly has shrunk into being a pure consolation trophy that many of the big clubs - with their bloated rosters - will use to "give a run out to" their peripheral players. Also, the FA didn't help by allowing it to be subordinated to the Premier League - the semi-finals, for example, used to have a day to themselves without any league action programmed.
Winning the FA Cup still gets you into
Europe's consolation bracket the Europa League, so there is that. But the big teams focus on the Premier League because that's big money itself, plus potential qualification into the even bigger money - and increasingly misnamed - champions league.
Another boon of the champions league is that qualified teams get the pick of free agents over the summer, as players want the exposure of that tournament so they can earn even bigger contracts and more endorsements.
Lastly, FIFA's Financial Fair Play rules put a limit on transfer spending based on your revenue. If you do well in the Premier League and also in Europe (e.g. Man City), your revenue is going to be much higher than teams with whom you compete who do not do either (e.g. Crystal Palace), so you get to spend more without falling foul of FFP. That means you can use your bigger spending allowance to outbid lesser clubs for the better players (which they then stockpile in their reserve squads and "give them a run out" in the FA Cup).
Basically, is completely rigged so that the rich get richer. It's if Trump ruled soccer -
which he sort of did.