Efficacy of model depends on scaling?
The answer to your question is: yes, efficacy of a model depends on scaling. It's very important to scale your variables in the right range and combine them with the right activation function.

The reason is the following: the power of Neural Networks is due to the fact that they can learn any non-linear regularity of your data. This depends on the use of non-linear activation functions (tanh, ReLU, ELU, you name it). However, most of activation functions tend to behave in a non-linear way only around zero. Take the plot of a ReLU, for example. If you move further away from zero (in both directions) the function becomes very "linear" (i.e. its derivative is a constant).

All common activation functions tend to behave like this: non-linear (i.e. very powerful) in the locality of zero, and very linear (or flat) further away from zero. That is why all data are usually scaled in the [0, 1] or in the [-1, 1] range. In this way, activation functions can give their best, and Neural Networks can learn all the most complex patterns in your data.

When you work with CNNs, for example, most of pixel data come in the [0, 255] range. This is very bad for all activation functions, since between 0 and 255 pretty much any of them will look almost completely linear. In this way, your CNN wouldn't be able to learn much.