FA Cup .... I'm a romantic when it comes to football, not a realist. Of course teh CL spot is FAR more valuable, blah, blah blah. As a proud achievements go, finish 4th or actually winning something ..... no contest, gimme the Cup!
While I'd love the fun of seeing Brighton in Europe for a season, a cup is something the club would be able to celebrate forever. So I'd go FA Cup too.