The standard 'rubber' hoses, over time deteriorate and flex or ballon if you like, this will give you a softer pedal.
The braided hose is still a rubber hose but the steel braiding over the rubber stops the 'flexing' and thus giving a firmer feel to the pedal.
Another thing of note is brake fluid, its hygroscopic which means it can absord water and over time it will, this will also give less feel to the brake pedal.
This really needs changing at least every two years or so, if you have old rubber hoses and old fluid, changing to braided hoses will mean bleeding the brakes and putting in new fluid, so you'll notice a difference right away.
You'd get a new pedal feel/better braking fitting new standard hoses and fluid but whilst your doing it you might as well fit braided hose.
I changed the fluid on my track day car every year and have fitted new rubber hoses twice as i could get them for about £7 each from the local motor factors.