Sorry, AEO= All Engines Operating and OEI = One Engine Inoperative.
The key to what I was getting at is what conditions you need to accelerate under.
Let's assume two aircraft, one with a VR of 130 knots, a good T/R but shoddy brakes, the other with a VR of 150 knots, a poor T/R and good brakes.
Takeoff distance has to account for both the "go" case, where an engine fails at V1 and the balance of the takeoff is conducted with one engine inoperative, and also the "stop" case, where the aircraft has to reject at V1 and halt on the runway. The higher I set V1, the easier I make the "go" case (because I'm closer to takeoff speed) and the harder the "stop" case (because I'm stopping from a high speed). Conversely, a low V1 makes the "stop" easy but the "go" hard, because I have to continue with one engine inop.
So, to be somewhat extreme about the example, I can conceive of a low T/W, good brakes a/c setting V1=Vr, while a good T/W, bad brakes a/c will set V1 as low as it can (basically, close to Vmcg). In such circumstances its possible for the bad T/W aircraft to still have good performance in terms of certified data, even though day-in/day-out the good T/W a/c will of course be more sprightly. Because it's the failure case where the two aircraft are balanced, and you (hopefully) don't see that too often.