Information processing is faster, up to a point, during the "alarm" and the early "resistance" phases of the Stress Response. During the later phases (exhaustion and recovery) it is dramatically slowed. During the "time standing still" phenomenon (which is reported in the Alarm-Resistance phase) there is a pituitary release of ACTH, to the adrenal glands which pour out adrenalin. Small vessels constrict, diverting blood from extremities to heart (which speeds up), lungs, major muscles. There is an almost instantaneous increase in liver output of glucose for the brain, and the brain changes the "mode" of thinking. This mode change is from conceptual-abstract thinking, to very focal practical thinking (survival thinking). It is accompanied by reports of "time standing still". Hearing is thought to become more acute, and pupil dilation makes vision more sensitive.
..after a while (which varies from person to person) the body moves into the resistance-recovery stages in which cortical processing is dramatically slowed.

So, everyone is right.. and wrong. There is speeding up.. there is slowing down.. of thought processing. Just depends on when you're measuring.