Provided 4th place actually gets you CL football then 4th place. (Spurs

)
Every. Single. Time.
If there has to be a choice between the two. Last season I'd probably have been split, a trophy is a trophy, but to compete in modern football quite simply you need CL football. Whether it be the money, or the prestige. Or the music. I don't see why there always have to be a trade off between a trophy and CL though... do both. You've had plenty of chances over the last few years to win the League or FA Cup that wouldn't hurt your league chances anymore than the crushing inevitability of going out in the SF.
As much as your situation of being in a rut and an all-to-predictable collapse is frustrating, 8th place is much, much worse.