As for me, I am of two minds, for two separate situations:
Where shorts are concerned, I agree with John. I have no doubt that the best short cartoons I love were all evolved from storyboards generated from the hearts, minds, hands, guts and mouths of cartoonists. These people just happened to also be natural born writers, even if they never got within shouting distance of a typewriter. As for experience, I've storyboarded my share of 9 minute TV episodes and it is always the most productive when the script is loose (prefreably an outline) and open to liberal interpretation. Generally the tightest, most over-written and demanding short scripts have tended to be the worst, from inception to outcome.
Most of my career has been in features though, and I have a minority stance here: I am actually in favor of full polished scripts, written in advance of the storyboard process. A lot has been made of the fact that the most of the classic Disney feature stories were worked out piecemeal on boards, developing from a key sequence somewhere in the middle and working out in both directions from there. All evidence indicates SNOW WHITE and PINOCCHIO were done this way, and even later pictures like CINDERELLA and JUNGLE BOOK. But conversely, there is also the account given that Bill Peet wrote a full, standard screenplay of 101 DALMATIONS before he embarked on storyboarding. It seemed to work out pretty well there. And there were hybrid attempts in between.
However, I believe it is all but obvious that Walt Disney's uncanny story sense and his innate and intrinsic intuition of general audience taste played no small part in all of these cases. And it should also be noted that even he was not infallible, even by his own assessment.
So in the absence of such a person, I believe in full, detailed feature screenplays. That they be good ones should go without saying, but that turns out to be a surprisingly subjective topic, although I don't know why. It should seem that a good script reads well to the majority of people and a bad one doesn't but for some reason it isn't always the case. The best positive example I can give from my own experience (and I don't mean to keep harping on this picture) was THE LITTLE MERMAID, which was scripted by Ron Clemments and John Musker. I remember reading a second draft that was so solid that it was unbelievable. You could just see the whole thing in your head as you read it: it was funny, heartfelt, gripping... Although the songs hadn't been written yet, Howard Ashman had made his input to the script as well and the song sequences were described in enough detail that they clearly promised what was delivered.
Metaphor time: A short film is like getting in the car and saying: "Let's go get some ice cream." Unless you are in the middle of nowhere, and even if you are a stranger in a strange city, you can probably drive around a bit and find a place to get ice cream, maybe even spectacular ice cream. If dad gets too anal about which streets to take, what toppings are and aren't allowed, etc, it's going to take all the fun out of even the best laid plans, however. Conversely, making a feature is more complex: you're getting in the car and saying: "I want to take everybody on a mind-blowing, two week vacation." With no map and no real idea, you might succeed, but you might just as well drive around aimlessly for weeks and get nowhere particularly exciting. It seems to me to make far more sense to commit to a destination and plan an explicitly favorable and scenic route, maximizing your budget regarding expenses like gas and lodging, etc. You can certainly be open to scenic sidetracks and shortcuts, but in the end, you will at least arrive where you intended. Your intent may turn out to be disappointing, but even if you failed, you failed on your own terms. It seems that taking the random route you are hoping to succeed by sheer luck. Seems like that is what they invented casinos for.
It should also go without saying that even an excellent script need not be a straight jacket for the story crew and as such, on MERMAID, the storyboards contributed considerably to the evolution of the film. A lot was improved, deleted, expanded etc. over the course of storyboarding and editing, but the script was the best foundation I have ever seen and it still holds up today. BEAUTY AND THE BEAST was fully pre-scripted as well, but my recollection was that it underwent a great deal more enhancement at every step beyond that point, from story to recording. I can certainly attest that David Ogden Stiers ad libbed some very funny material that made it into the film and story talents like Roger Allers, Brenda Chapman, Kevin Harkey and the directors Kirk Wise and Gary Trousedale contributed extensively too.
During ALADDIN, after a first pass was done and discarded, animation production got underway with only a partial story and as a result, the old "triage" method began to work its way to the fore again. The finished film is still solid, but I do recall a lot of energy expended on scenes, songs and ideas very late in the game that never quite panned out. Had these issues been worked out ahead of production, it may have been more ideal for everybody. On several subsequent features, my impression is that the scripts began to get less specific, sketchier on crucial details, more schematic, and as a result the story was often in shambles right up to the eleventh hour of production and then somehow came together at the last minute. I think the industry got addicted to this rush and tends to follow that practice in pursuit of it ever after. Even though as a road to success it has turned out increasingly to be the exception and not the rule.
I've had a hand in the stories to one extent or another on many of the nearly 20 features I have worked on, and I have even gotten writing credits occasionally. For the most part, my most extensive writing contributions were done in cases where it was piecemeal, either by the studio's choice or production necessity. I won't go into detail, since these were all collaborations and I don't mean to speak for everyone involved, and the amount of overlap is considerable. As a method, however I don't agree with the piecemeal approach to a long form story. I've often compared it to building a house from the inside out with no blueprint: you can't see it until it's done and that can turn out to be too late. There are some live action filmmakers who can improvise their way to success (Robert Altman springs to mind) and maybe it isn't impossible in animation either. But unless the movie is supposed to have an anarchic, improvisational feel, it is just too much to ask of an animation crew to spin their wheels any more than necessary.
Or as one astute collaborator put it (in regards to the piecemeal feature approach): "I thought it was supposed to be 'Ready, Aim, Fire!' not "Ready! Fire! Aim!' "