The difference in outcome could be negligible or vast depending on your attention to detail while brewing.
Variables that will affect your outcome (just a couple)
heat sources/thermal mass - you will be using different heat sources, so your heat up times will be different, your cool down times will be different, your temperature swings during the mash from temperature inputs will be different. The larger vessel will potentially hold temperature better due to the increased grain/water mass. One will happen outdoors one will happen indoors so ambient temperature will play a role.
efficiency/crush - since your volume of grain will be different any inefficiencies due to crush will be harder to correct in the larger batch, any inefficiencies due to mash temp will be harder to correct in the larger batch and these corrections will affect your final product (assuming you correct with DME/LME).
All of that malarky above stated, I've brewed in VT on an electric stove with a 18qt pot and a 12qt pot, in Brooklyn, NY on a gas stove with a 18qt and 20qt pot, in CT with a 32qt, 20qt, and 18qt pot set up; if I do the same recipe and use the same water, my beers come out generally the same. I accidentally tested this with my "Vermont Maple Porter" I used 6 gallons of Vermont pure water, some Grade "B" maple syrup from the same farm in Vermont, and the same grain bill (although from different sources) it started out as a nostalgic recipe when I moved from Vermont to Brooklyn, then when I made it again in CT I realized it was more of a control batch. Each time, it is more or less exactly as I remember it, however i haven't made it back to back (i.e. made it in Brooklyn, then moved to CT and made it right away), however, as a control, it's pretty spot on; unless my memory is not to be trusted.
So yeah, I honestly think you can make very much the same beer on two separate systems if you scale the recipe properly, and recreate your process accurately - if you overshoot by 2 deg during the mash on your smaller system, do it on the big system, etc.
DO IT and come on back and tell us how it went