According to City of Data, Sprint is a +100% run speed bonus, which brings the base run speed from 1.0 to 2.0. It was split into a 50% enhanceable and 50% unenhancable part, but totaled 100%. It also gives a 10% jump height boost, which Paragon Chat does imitate even though it's barely noticeable.
Probably the reason it seems faster than on live is the fact that for a couple years on live, everyone had inherent Swift, which is a +35% run speed boost, more if you put an enhancement into the free slot. The difference between a run speed of 1.35 and 2.35 (74% increase) seems less than the difference between 1.0 and 2.0 (100% increase).
In other words, Sprint feels faster on PC because the normal run feels slower than people are used to.