In transport drones you put down "requester" building, select up what you need, you put items into storage building and they will just handle everything rest for you. Bots carry 1 stack of items (or 1000 fluid) - by default. Than there are researches to upgrade their carry capacity up to about 5stacks? 6? I'm not sure. Those drones require liquid fuel to operate - I believe petrolum gas by default.
I would say Transport drones feel like something in between bots and trains. Compared to trains they need less space/can't colide and don't need station conditions, but carry less items and are slower. Compared to bots they need route that take space - on land, they need fuel instead of eating energy but they carry much more items per trip and are earlier technology.
Unfortunately I cannot tell you much about logistic carts mod, I have very little experience, but looking on test world it is definitely not like logistic bots. It's quite complex to set up, they transport way more items - they are in "junk train" weight category, if I might tell so. I would say they are very close to being like trains, but have some smart behavior that you can set up, they can interact with circuit networks in very interesting way. They can drive offroad, but they will crash into anything that has hitbox - so be careful not to put anything on their path, except underground belts or something that doesn't have collision.
I would say UPS wise, both mods should be very decent. First one is basically logistic bots, witch require some pathfinding, but for exchange it carry lots of items compared to bots, so that save UPS, they don't colide nor need to calculate energy per tick - like vanilla bots do. Second mod also has a lot of UPS improvements - even bigger storage to combat fact that they are slow. They don't need to pathfind and there are many other optimalizations.
