There are two main things about tranny fluid:
Transmission fluid is checked when it's hot (up to running temperature). As the fluid gets up to temperature it expands. If the fluid is cold, it won't give the proper level reading, thus overfilling will ensue.
One of the main fluid compartments of the transmission is the torque converter. When full, the fluid level of the torque converter is much higher than is the level of the pan (almost entirely above the pan in most cases). Due to this, when the engine is stopped, a significant amount of the fluid will drain down into the pan, showing the wrong amount of fluid on the dipstick. With the engine running, not only is the transmission paths filled with fluid, but the torque converter is as well. Then a check of the fluid will give you a proper level.
Checking engine oil is a lot different. It needs to be checked when it's in the oil pan. In order for it to be in the oil pan, it needs to drain after it's been up in the engine. This takes a little bit of time. Engine oil doesn't expand as much as transmission fluid, so can be checked hot or cold. While engine oil is important to how an engine operates, the level isn't as imperative as transmission fluid. Transmissions are very sensitive to line pressure. As you get more transmission fluid into the transmission, the pressures rise. If left unchecked, the fluid will find an escape hatch somewhere and that somewhere is usually a seal. Blowing out the front main seal (or where the torque converter rides) requires a transmission pull to fix. This isn't something you want to do every day.
Engines don't have the pressure effect which transmissions do. The pressure is regulated at the pump and mainly needs to have oil flow in order to operate efficiently. Most engine manufacturers are good down to even 5psi of oil pressure. There is also a lot of space in an engine for oil to hide. As oil gets pumped around, it sticks to walls and is all over the place. It needs to drain back into the sump, thus the 5 minutes of drain time. Not everything will drain down, but the vast majority of it will. This isn't how every manufacturer likes to have it read, but leaves things in a pretty good state as far as the level goes.
I don't read this as a discrepancy in either case. I look at it as how they are designed/engineered to be checked.