Yes, it is a very wise choice to not use industrial detergents when washing the clothes of your second son. For example, by personal experience, polyphosphates and pyrophosphate can have quite aggressive on the skin, and some additives that can even be sensitizers (exposure can make a person become very allergic to it in the future, even when exposed to extremely minute dose of the additive) !
The two formulas are similar actually. But Delphine (@delph-in-holland) is the expert on the practical effects, I'll let her comment :-)
Please, let us know how happy you are with the results of your first formula !
I will surely write some post on the subject in the future ;) Your expertise had been very helpful to understand "why" it was better like this! Thanks to you!