I do know english football but todays FA cup is not nearly as prestigious as it once was and it became a consolidation prize for PL losers, sry but that's just the way it is, maybe not to Hull City or Arsenal but ask the rest of PL teams and the would gladly change FA cup for PL title and a chance at Champions League.
Of course they carry more weight, they are bigger cups. But everyone who does not win its said its the mickey mouse cup, but as soon as they win it, it becomes the most important one. I would rather finish 4th and have the FA cup then finish second and have no cups at all.
The FA cup is one the best cups in my opinion, you get the likes of hull and wigan who do very well in them and beat teams like Chelsea and City.
I really don't see Chelsea winning any cups in the near future, City will always have a better team. Chelsea don't have what it needs to win the title. Costa will not shine in the Premier League, Fabregas is no where near what he used to be and Luis is an average left back.