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.