TI's got a tool, named WEBENCH which can make a lot of charts and calcualtions for you. Here is its output with your parameters in pdf.
Let me highlight the one about the efficiency. The simulations shows that this IC has a better efficiency when Vin is 20V, but this difference is not that much.

It is not just the Vin that matters, if you change the supplied current from 200mA to 3A a different efficiency chart will be shown. In this case the Vin = 30V is the better choice.
Usually, there are similar charts in the datasheets if tools like this are not available.
If you only need 200mA, you should choose converter which is capable of, let's say 300mA maximum current rather than 3A, efficiency is better near the max current. Another converter, which can drive max 300mA, LMR14203's efficiency chart:

It is again the worst at 30V, but it is around 88% while with the LM2596 it is 79% which is a significant difference. On 20V it is above 90% which is pretty good.
The circuit that you linked is a horrible voltage converter. It has no feedback in the circuit to dynamically adjust the duty cycle to regulate the output voltage. The additional circuit on that web page showing to use a power transistor with a zener diode to compensate for the short comings of the 555 circuit is also a horrible approach.
There are a plethora of available switching power supply controller chips and modules available that will do a far more superior job of converting the voltage from 12 to 5 volts. Get one and use that instead.
Best Answer
I'm assuming you have an input voltage of 24 volts (say 23 volts to 25 volts) and you want two outputs; one at 5V (and 5A) and one at 12V, 5A.
The simplest (possibly) way involves going to Linear technology's buck converter page and plugging in the numbers for both outputs. The dat entry area above should be setup for an input voltage matching your requirements and 12v for the 1st output. It suggests many devices to choose from.
The LT8612 looks good for 5V (or 12V) at 6A and the LT3845A looks able to provide 12 volts at over 6 amps. There are others on the page also worth looking at.
Should you be wanting a bargain-basement low cost product you didn't say so I went for the technology that I know to be probably the best and one of the devices (LT8612) I've used successfully in a couple of designs.