The professionals disagree (in a very long-winded manner). Longman seems to present the natures of the two words concisely and in a way that is easy to remember, and its presentation seems to best represent the way these two words are actually used these days. Read Webster's and Fowler's if you want, but their explanations are quite complex and confusing, and not 100 percent representative of current usage.
Longman Lexicon of Contemporary
decided: definite; clear. 1) There has been a decided improvement in his health / the weather. -ly [adv.] His health has decidedly improved. 2) having formed an opinion; made a decision: She was quite decided in the matter; she would go and no one would stop her.
decisive: deciding easily and forcefully; causing something to be done, finished, won, etc. He is very decisive in business. The battle was decisive; they won the war.
Collins COBUILD Dictionary
decided: 1 Decided means very obvious and noticeable. He thought that their plan held very decided dangers. 2 If you hold decided views about something, you have very strong and definite opinions about it. She has very decided views on abortion.
decidedly: 1 Decidedly means to a great extent and in a way that is very obvious. The men looked decidedly uncomfortable. 2 If you say something decidedly, you say it in a way that lets people know that you have strong views about something and are unlikely to change your mind. 'It's time things were altered," said Mrs. Moffat decidedly.
decisive: 1 If a fact, action, or event is decisive, it makes it certain that a particular choice will be made or that there will be a particular result. Three factors had a decisive influence on the paper's editorial policy... The government fought two decisive battles against the miners' union. <> decisively She defended her seat and was decisively re-elected in the general election. 2 If someone is decisive, they have or show an ability to make quick decisions in a difficult or complicated situation. He isn't decisive enough to be a good leader. <> decisively 'That's a job for Peter,' she said decisively. <> decisiveness Will he ever learn to show decisiveness at work?
Webster's New Dictionary of Synonyms
decided, decisive are often confused, especially when they mean positive and leaving no room for doubt, uncertainty, or further discussion. In this sense the words are applied chiefly to persons, their natures, their utterances or manner of utterance, their opinions, or their choices. Decided implies a contrast with what is undetermined, indefinite, and neither this nor that; thus, a decided blue raises no question of its greenness or blackness; a decided success so far overpasses the line between success and failure that no one can question its favorable termination; a decided answer leaves no doubt of a person's meaning, wishes, or intentions. When applied to a person's character, expression, or movements decided suggests such qualities or outward signs of qualities as determination, resolution, and lack of all hesitation or vacillation <The mother was a decided person to whose will everyone in the family submitted> <He has very decided opinions> <I see too many ways of saying things; a more decided mind hits on the right way at once-Ward> <Then with a decided step she turned toward home-Wharton> Decisive, on the other hand, implies an opposition to what is unsettled, uncertain, or wavering between this and that (for this sense as applied to things see CONCLUSIVE). When used in reference to persons it implies ability or intent to settle or success in settling a controverted matter once and for all <This was enough to determine Sir Thomas, and a decisive "Then so it shall be" closed that stage of the business-Austen> <She stood up and surveyed herself in the pier glass. The decisive expression of her great florid face satisfied her-Joyce>
Fowler's Modern English Usage
decided, decisive. Decisive is often used loosely where decided is the right word, just as DEFINITIVE is a common blunder for definite, and DISTINCTIVE an occasional one for distinct. A decided victory or superiority is one the reality of which is unquestionable; a decisive one is one that decides or goes far towards deciding some issue; a decided person is one who knows his own mind, and a decided manner that which comes of such knowledge; a decisive person, so far as the phrase is permissible at all, is one who has a way of getting his policy or purpose carried through. The two meanings are quite separate; but, as the decided tends to be decisive also, it gets called so even when decisiveness is irrelevant. Examples of the wrong use are: The sergeant, a decisive man, ordered... / A decisive leaning towards what is most simple... / It was not an age of decisive thought. / Poe is decisively the first of American poets.