Construction // In terms of handle drop, I find both bags fit very comfortably over my shoulder, even while wearing a winter coat. The Longchamp has a longer drop than the Madewell, so I find it more comfortable to carry when stuffed. Additionally, the Longchamp is water-resistant and has a full zipper, which makes it far more versatile in terms of when I can carry it. I love the leather on the Madewell, it's so sturdy and the color is beautiful, but the open top can be limiting. Winner - Longchamp
Size // Both bags fit roughly the same amount of things, but because the shapes are different, the ability to over-stuff tips this battle in favor of the Madewell tote. Both bags fit everything pictured above with room to spare, but because the Transport has more vertical space, I find it much easier to shove a cardigan/snacks/dog supplies etc in the top. Winner - Madewell
Features // Both bags have a single built in pocket. The Longchamp's pocket is much smaller and once my iphone 6 is in there, not much else will fit. The Madewell, on the other hand, has a much larger pocket that fits all kinds of stuff. I appreciate that both bags are minimalistic in look and come in classic colors and can be personalized. Both are fairly easily cleaned, though the nylon of the Longchamp is almost impervious, which I appreciate. Winner - Longchamp
Overall // Never in my life will I regret purchasing a tote bag, and I truly believe both of these bags are worth the price. In general, I think that the Longchamp is more versatile - between the zipper, the water-resistancy (word?) and the plethora of colors, it's the bag I would re-buy first if both were to die in a fire.
Buy my version of the Madewell Transport Tote bag here and the newer version here (zipper! more pockets! more colors!). The Longchamp can be found here in tons of colors and a few sizes (this is my favorite)