I think the budget totals posted are very illuminating. It generally seems accepted that Paramount didn't spend enough money on TFF, particularly on visual effects, but the numbers don't bear that out.
TFF had a 43% higher budget than its predecessor, made just two years earlier. That's quite a sizable jump! Additionally, it had a 27% increase just on visual effects alone.
I think, as has been pointed out, the problem was more that the dollars were not spent well. Going with Associates and Ferren was the biggest mistake. Not budgeting adequately for the ending you wanted to shoot was another. Yes, I understand that you can't have it all, but why spend so much money on, for example, building a full size shuttle bay set, and then not having enough money to actually film the ending you wanted?
Edited to Add: If you read the article linked to above, Winter himself essentially admits that they made bad decisions with the money. The story has always been that ILM just wasn't available to do the effects, but he admits they felt ILM had taken advantage of them and so they chose to go elsewhere, and then also admits they made a really bad selection in choosing Associates and Ferren.