I prefer controller for all Spidey games, except for SM200 - wich works better with keyboard and SM2PC - where mouse is requiered for it to work.
Personally, keyboard+mouse feels very uncomfortable. You have one hand on the mouse for the occasional swings and camera movement and left hand for everything else, which makes it so busy with doing too much. For that, you can also map Swing and Web keys on keyboard and play keyboard-only for most of the time.
Bare in mind that using an Xbox360 controller (may be the same for One), when LT and RT are pressed together, they cancel each other. That's because the triggers have "Z axis" to enable sensitivity for how much you press them down and when pressed together, the value is 0, so the game thinks nothing is pressed. Using RB and LB instead is just as good id not better.
