which is important?

Neither of these points of view excludes the other.

English has one of the largest vocabularies of any language on earth -- close to one million words in an unabridged dictionary. However, most people who are fluent in the language are familiar with only a small fraction of this huge collection -- a few thousand at most. But what good is knowing the words if one doesn't know how to properly string them together in a sentence? Noddy24 is absolutely correct -- the two things are not mutually exclusive.

Language is an Art of communication... in which combinations of sounds (words) are arranged in such a manner as to convey meaning.
Simple elementary communication requires less vocabulary and grammatical expertise than the realm of subtlety and nuance.

Some people are forced, through inability to hear or speak, to communicate via hand signs... experience, skill and creativity all make a profound difference in the level of communication attainable.

The richness of the English vocabulary necessitates a fairly rigorous, tightly structured grammar. Note I did not say "Well Structured", or even "Logical" grammar - English grammar has almost as many twists, exclusions, exceptions, and loopholes as do the millions upon untold millions of pages of laws that are written in the language. But it does have an established - if somewhat arcane - structure.

It is through deft execution of that structure, in conjunction with the astounding vocabulary available, with which, at the author or narator's choice, may be achieved absolute precision, maddeningly vague nuance, delightful whimsy, the sternest of pedagoguery, and everything in between ... often even using the same or very similar words, varying only their placement within sentences, punctuation, inflection, and/or context.

If you follow the guidelines of any of the "Style Books" of major newspapers or universities, you'll prolly not go far wrong.

Could you communicate solely by vocabulary lists? Or by the elegant bare bones of wordless diagrammed sentences?

Interesting you should mention sentence diagramming, noddy. That's something which seems to have fallen from favor. Pity its not more widely taught.

equally important is my vote

Timber--

I just finished an essay in the "Readings" section December Harper's, Sister Bernadette's Barking Dog by Kitty Burns Florey.

Like you, Ms. Florey is a devotee of diagramming sentences. There are at least two groups of grammarians in this world: Those who delight in the precision and order of sentence structure expressed in diagramming and those who consider the procedure a time-wasting, mechanical exercise.

Of course, there is a third group that wants no part of English Grammar.

I'm in the second group--I can diagram--and I can teach diagramming-- but when I have a piece of ornate prose correctly staked out on a page of notebook paper, I feel satisfaction, but no great delight.

For the visually minded--which I assume you are--diagramming is a delight.

We need delight in this world, particularly in English classrooms.

I guess I've always sorta gotten a kick outta takin' stuff apart and puttin' it back together again - sometimes again and again and again - to figure out how and why it works, why someone thought to do it that way, and even to see if I can figure a different way to do it. Diagrammin' is just a form of that, to me. Other folks seem to assume somethin' will work just 'cause they think it will or want it to. I think that sort create a lotta problems for themselves, and others, whatever the pursuit.

Timber--

A lot of Plato's philosophy is a bit abstruse for my fancy, but one notion that makes great good sense is the invincible balance of mathematics, the music of the spheres.

I don't register celestial melodies from math or diagramming sentences. My gleeful harmony comes from word play and wit and the complexity of human nature.

You have your music and I have mine--and the world is a glorious place.

Yup. Pretty much. Some folks ain't got much musical talent though - they're mostly just loud.

what is this diagramming? we may do it here by another name but I've never heard of diagramming

Diagramming Sentences

Another good treatment, from the excellent Guide to Grammar and Writing Website.