It is hard to make this theoretical because the Sox DID win it all. And besides, it is a bit of a false choice. But either way:
1. I like baseball. When the team I have cared about more than any other (across all sports) plays good baseball, I am happy.
2. There are not many other things to follow sports-wise during the summer. When the Sox stink, it's a real drag. (it infects my ability to give a crap about my roto team - or to even watch baseball)
3. The playoffs are a crapshoot - while you'd like to be able to invent a champ out of thin air, I can only remember that actually working out once (the 2009 Yankees). You need luck, the right bounces. The Red Sox three titles were sort of rare in that they were probably the best team in the league all three years. (and beat the 2nd best team in the league all three years) Get multiple bites of the apple and see what happens - after all one of the Cardinals titles came with the worst team to ever with a title.
That the Red Sox whiffed on getting a bite of the apple so badly in 2012, 2014-15 is a real black mark on their record - you can't unsee that. This does not mean I am ungrateful for the three titles. But it does mean that within the context of whether I'd rather be the Sox or the Cards of the last decade, the Cards could be argued quite easily.
Being a Red Sox fan from 1970 to 2003 was not difficult - the team was almost always good! There was heartbreak which stinks - and some years stunk even more. The reason it was so easy to yammer about a curse is that the Red Sox WERE good - the idea that they would get to Game 7 four different times and lose is mystifying. But I'd recommend that being an Expos fan was slightly harder during that time frame - the angst of the pre-curse Sox fan (let alone post) is why other fan bases hate us.