A very important point to this is not how much runway it uses to take off.....it's how much runway it uses to STOP.
As correctly pointed out both aircraft use the assumed temperature method to develop the minimum required power to get airborne safely. So at an airport like MIA both aircraft could probably get airborne in, say, 40% of the runway lenght. Maybe one would beat the other hands down....I don't know. But thats not important.
If you work backwards from the end of the runway and figure out where each aircraft must apply max braking at V2 (go...no go decision speed) in order to stop by the end of the runway then you will find the 738 will require less runway to stop than a 757 (it is much lighter!!). So when we derate the engines, the ideal is to derate as much as possible thereby saving the engine life as much as possible. However, the most you can derate is to the power setting which will get you to V2 at the point where you have enough runway to stop for your particular aircraft. This will change depending on temperatures, weight, airfield elevation etc etc)
Therefore, all aircraft with cost concious pilots on board are not lifting off where 'they are capable of lifting off'. They are lifting off 'at the last safe point they can lift off'. Your observations go to prove that a 738 can stop in less distance than a 757.
You will see that some aircraft will lift off before a 757 even though they can obviously stop in a shorter distance. This is because with all aircraft there is a maximum to which you can derate. This is mainly because in the even of an engine failure you must have enough power on the remaining engine to carry on with the takeoff and climb after V2. So on max derate a Ba146 will still lift off before a 757 on full power (probably!!).
I have tried to explain this without getting too technical. Sorry if it sounds patronising to non flyers...and to the flyers, I know I left 99% of my perf course out...but I only have a few paragraphs to explain!! I know I'm out on a limb with the reference to being lighter but it makes the point!!!