The biggest difference for me is that の makes it a bit harder to pronounce when I speak and sticks out a bit in my head when I hear it. This difference goes away when の is reduced to ん.
I would say the following two sentences are practically interchangeable. I feel no particular emphasis in one over the other.
トムが行くなら、私も行きます。
トムが行くんなら、私も行きます。
なら could be rephrased using ば but の is mandatory in this case.
x トムが行けば、私も行きます。
トムが行くの/んであれば、私も行きます。
I understand this as meaning the function of の is already included in なら. You are already assuming a particular situation and describing that situation as you would when you use の.
[Edit]
If I had to nitpick a difference, I would say the version with の gives an impression that the described situation is already decided outside of the speaker’s control, as if to say:
トムが行く(ことになっている)のなら、私も行きます。
If (it is already decided that) Tom goes, I will go, too.
The textbook is probably referring to this feeling of the information coming from an external source, as opposed to the speaker coming up with their own assumption.
But again, you could say the same thing without の.
トムが行くことになっているなら、私も行きます。
So I would say the difference is mostly negligible.