This is my F4's rear brake hose. I have two questions here;
Is that bulge just after the banjo normal or should I get a new one?
Is there any advantage to buying a rubber line instead of braided? I mean, might the slight amount of give be just enough to help prevent lockup in a panic?

 

The bulge looks to be a natural flare from it going over the metal of the banjo although mine isn't quite that pronounced. If it doesn't have cracks in it from dry rot, it should be fine but certainly won't hurt to replace if you are feeling a bit sketched out...

As for braided vs. rubber, on the rear brake I see zero advantage to using braided other than as "flair" or, possibly, longevity. That being said, I don't have any experience with braided lines and am still running my stock rubber lines. I try to practice emergency braking on the regular and have yet to reach a point where I feel like my braking ability has surpassed what the brakes can do at full squeeze. YMMV...