I'd have to disagree. Great films can have low budgets or subpar special effects and still be great films. Conversely, a lousy film with a big budget and fantastic special effects is still a lousy film...with a big budget and fantastic special effects. (I'm talking to you, The Phantom Menace...)
What would a bigger budget have done for this film? More rockmen? New corridors that weren't just redresses of the Enteprise-D's? A Klingon ship that wasn't another reuse of the BoP? The Galactic Barrier being shinier? And alien fake-God who's more than just a floating head? None of these things enhance the plot of the movie or make the story any better.
True. TWOK was made on a much reduced budget from TMP. If the story is good enough and the director and production staff creative enough, they could make a good movie.
I do remember reading some of the reusing of TNG sets was not just budgeting reasons, though that was part of it. Some of it was Shatner wanted to show a link to TNG--in an ancestor sort of way. So that you could see the beginnings of what would become TNG. That was one of the reasons he hired Herman Zimmerman as the production designer along with the Okudas. That would be one of the few things carried over into TUC, with Meyer retaining Zimmerman as PD--again for some of the same reasons, budgeting partly and showing some transition to TNG.
On the other hand, budget or not, the special effects in TFF are just plain bad, and unworthy of any Star Trek film (or any non B-film for that matter). I don't care how much the budget was, the effects are just embarrassing.