The 10400 is 4 cells each sharing 2A so each cell is getting 0.5A. The Mini+ is 1 cell with 1A, and so the Mini+ gets noticeably hotter than the 10400. The 10000 would probably get a littler hotter than the 10400 as its 3 cells sharing 2A.
Golly, how to explain QC and USB 3....
This will make sense if you understand the Lithium cell recharge and discharge and then understand DC-DC conversion. Once you understand them then QC will make sense.
Charging Lithium cells:
The recharging of a battery involves forcing electrons into the material, those electrons repel each other (like charges repel) and when there are not many electrons in the cell it is relatively easy to force electrons into the cell. As the cell becomes full with electrons, it becomes increasingly harder to force more electrons into the cells. This is shown as an empty cell has a higher current input and the voltage potential is lower, then as you recharge it, the current has to drop off as the voltage rises. These last 2 sentences is very overly simplifying the physics but did i do that in one paragraph? This simple charge roughly shows the process.
The issue is USB is a fixed 5V so you then have the issue that the cells need a progressively higher voltage input as they charge, initially lower, then higher. How do you give the cell a varying voltage? How do you take 5V DC input and make initially a 3.7V to the cell and then slowly increase it to 4.2V to the cell? I will (again) over-simplify and show the basic electronics of how you change one voltage into another voltage of DC-DC conversion. Watch this video:
Inside the Anker Powercore there are multiple processes going on. When you recharge the Powercore it is taking 5V 2A input and making a lower voltage higher current in a flat Powercore (say 3.7V 2A) and progressively ends nearly full at 4.2A with a lower Amps. Then it then acts as a charger, it takes the 4.2V initially coming out of the cell and steps it up to 5V and then as the voltage from the cells drops eventually to 3.7V, the electronics step the voltage up to 5V.
The cells inside your mobile phone have the same problem to solve as cells inside Powercore. The mobile phone has a cell usually rated 3.7V, when your phone is flat, the cell in the phone is more able to be recharged faster, a higher current. All that QC does is take a much higher Wattage initially over the USB port and then slowly take less as the phone's cell becomes fully charger. This leads into lower phone recharge times. But how to do deliver higher Wattage? Do you increase the voltage or the current? If you increase voltage you risk a spark at the phone USB socket, if you increase Amps you risk melting the wire? Hence the phone and and the charger communicate and step the voltage, amps, in an algorithm which is proprietary to QC. Ultimately, however, it is just supplying more energy at the start and less at the end, it is just doing the boost converter role intelligently to the cell.
USB 3 is just the current (3.1) standard of USB and USB-PD with USB 3.1 has cables capable of handing higher voltage and higher current so you can drive more energy through the cable and port without sparks nor the wire melting. Ultimately, USB-PD is superior to QC because QC is about recharging a phone, while USB-PD is about much higher Wattage and high speed data transfer. Due to the proprietary nature of QC, it is hard to merge all of the electronics together in an Anker Powercore. One tends to get 1 QC port and a non-QC port and they share little. That tends to cause a higher cost product and physically larger. The future is more USB 3.1 and USB-PD but it will take time as there are not as many USB-PD devices to cause Anker to sell enough units. That will change through the next couple of years.
Think in regards of your device you buy and their charging needs, together, as an integrated system, of devices, cables, chargers. If you literally only have a phone, then buy the phone you want, it comes with a charger, of some kind of technology. Simple.
If you though have a phone, and tablet, and BT earbuds and portable charger, etc, then it becomes more complicated. What matters to you? Is it cost? Is it speed? Is it weight?