Stem length should not affect weight distribution, unless you're making the mistake of moving the saddle to fit the stem length. A bike should be fit with the correct saddle position, relative to the bottom bracket first and then the stem length chosen for a comfortable fit. The weight distribution is mainly determined by the saddle position.
If you have two bikes, with the saddle adjusted to place the rider in the same position relative to the BB, then a bike that needs a longer stem to get the same reach, would not change your breathing, power or speed. It would just have a little more weight on the front wheel, due to a slightly shorter front-center dimension. That bike might also have some toe overlap. A bike with a 10mm shorter stem should fit exactly the same, but probably has a little longer F-C, a little less weight on the front wheel and less or no toe overlap. That's the kind of difference I get between my Colnago (longer reach, 10mm shorter stem) and my LOOK. Both handle just fine on twisting mountain descents.