"Ineffectual" vs "ineffective"

Solution 1:

I tend to think of these as having a slight difference:

• If something is ineffectual, it is not having an effect right now.
• If something is ineffective, it has been shown not to have an effect in the general case or the current situation.
• If something was ineffectual, it wasn't working as of the time context of the sentence.
• If something was ineffective, it did not work in a particular past situation.

So, ineffectual in my mind refers to the state of it having an effect at a specific point in time, either right now or at some definite point in the past. Ineffective refers to the state of it having an effect in general, or during a given "event" in the past (which may not be given a definite place in the timeline).

Disclaimer: this difference is probably all in my head, it's just my opinion, no research to back it up.

Solution 2:

I neither agree nor disagree with the fine distinction made by @KeithS, but I think most people will side with OP's "intuition", and think both words "mean" the same.

The biggest effect of changing ineffectual to ineffective is that the sentence would be more "snappy" and "modern". Here's a chart showing the written usage trend...

It's my guess that in using the older/more established/archaic term, the writer primarily intended to add a touch of gravitas to his text, rather than because it conveyed something subtly different to ineffective (along the lines of any suggestions here, or indeed any others). This I think is a common device in "persuasive writing", which does appear to be the context.