There's a role for both. I'll give my personal take.
For improvising it's fake books all the way. I find that I don't really improvise freely with sheet music, and anymore, when I play I want to be improvising. And even if I want to play something set, it's something I want to practice and memorize, like the head and a finale.
Sheet music, for me, is largely for practice (putting aside things like classical or set arrangements just for fun sometimes).
And I have two uses in practice.
The first is for technique practice. Sheet music usually has a good mix of complex techniques on the fly, so it's good practice for me to run my fingers through them and get them trained to do things I wouldn't normally play myself. The whole point of technique training is venturing out of your comfort zone into techniques you don't normally use, and sheet music gives you that, especially transcriptions of people whose sound you want to emulate and learn from.
The second is for improv fodder. What I like to do is get 3 or 4 or 5 arrangements of the same song, and I'll basically collect ideas for the passages. Push come to shove I can just use one in an improv, but the idea is I tweak the idea to make it my own, and they're just fodder to jump start my creative thinking. I can start with a few sheet music ideas while I'm improving and then my playing can start going its own direction. Sheet music is good for that because usually arrangers come up with some very creative ideas if they're putting something down on paper.