The OEM would have a smooth, initial bite, but I wouldn't say they are greater or have more initial torque than the Hawk HPS. It is true, as far as performance pads are concerned, Hawk HPS are considered having a relatively low initial bite - and like more performance pads, that initial braking event of the day will be weak until the pads clean off the rotors. OEM will brake the same way from day to day. But compared to OEM ceramic composites - the HPS does grab the rotor faster, with more follow up torque. The OEM smoother bite might make it "feel" like greater torque. This will quickly change once you get the brakes smoking hot or trying to brake from high speed.
A racing compound pad would even be more aggressive, bite-wise, assuming the pad was up to temperature. Some race pads aren't effective until they start to get up to temperature, before then, they squeal and have poor pedal feedback (ie, can't tell how much bite there is, can lock up the brakes with little to no warning, pedal is spongy where you can't vary the amount of pedal force or too stiff like you are stepping on a bag of concrete but with zero brake feel).
As for Racing Brakes pads - from what I've heard, they've actually worked with Hawk on some R&D aspects - so they would be very similar products. Their ET300 would be equivalent to the Hawk HPS, their ET500 would be more like Hawk HP+, their ET700/800 series are considered more competition than streetable pads (ie, very agressive street pad) which would be equivalent to Hawk Black or Blue pads, their ET900 is a full fledged race pad, like the HT and DTC series of Hawk pads. I have not used RB pads myself, but they come highly recommended. Not sure if they have fitment for a Corolla - last time I checked, they did not.
I think you'd probably stand to gain some better braking performance with a quality DOT 4 brake fluid like Castrol SRF, Motul RBF 600 or ATE Super Blue for higher boiling temp capability and stainless steel lines for less brake line flex/expansion. The other parts - sliding calipers, brake pedal, and master cylinder - will make up the rest of the slack in the braking system. But by doing fluid, pads, lines - you got 70%-80% of the possible "slop" in the system taken care of.