Among aircraft whose nominal cruising speeds are within a couple of percent of each other, which includes all modern passenger jets, that number is likely to be way down the list in terms of who actually arrives first. For one thing, an optimum (in terms of fuel consumption at a given speed, or equivalently, speed at a given fuel consumption) flight path involves gaining altitude as fuel is used. Whether or not one can do that depends on what other traffic is in the area, such as another aircraft already up there where you'd like to be. If that other aircraft happens to be the nominally-slower one that took off a few minutes earlier, there goes the infinitesimal edge that a trivially higher cruising speed spec might provide.

And that's assuming both aircraft were given exactly the same routing. If they weren't, they'll hit different winds and weather, and all bets are off.