Wikiversity says the following about long vowels in Japanese:
A long vowel takes two morae. In rōmaji it's written with a macron: ā, ī, ū, ē and ō.
In hiragana, it's written with an extra "あ" (a), "い" (i) or "う" (u) depending on the vowel. In katakana, it's marked by appending a dash-like symbol "ー".
Why are they represented differently in hiragana versus katakana?
Let's start by saying that not all words follow this rule. According to Japanese Wikipedia, a number of words are written in katakana but with doubled vowels, as if they were written in hiragana (in which they can be equally well written):
例：シイタケ、フウトウカズラ、セイウチ、ホウセンカ、オオバコ
But these appear to be words that have kanjis, and fallen out of use. The "dash" is used mainly for foreign and mimetic words:
例：ニャーン、テーブル
It would thus appear that the dash is mainly used in "new" words. I could imagine as being a consequence of the use of new phonemes, such as ティ which would look maybe weirder when elongated into ティイ than ティー.
As for the origin (I take this directly from the Japanese wikipedia), it is said that it was invented to transcribe foreign languages, but it appears (according to 国語学大辞典{こくごだいじてん}, literally "great dictionary of japanese language") that it was first used by a scholar of the Edo period and that it became commonplace in the Meiji era.
The symbol itself apparently originates from:
引く音の「引」の右側の旁（つくり）から取られたという説がある。
i.e. The right part of the kanji of 引{ひ}く, "to pull", as in "to stretch the sound". Note that this is a theory.
Apparently, in 1900, the ministry of education tried to enforce a new rule, by which all long vowels (in kanji pronunciations and interjections) would be denoted by a dash -, for example: 校長｛こーちょー｝ (principal of a school). However, this ordinance was quickly repelled, in 1908.
What you've seen on Wikiversity is just a superficial explanation (or for beginners?).
The spelling rule doesn't reside in hiragana and katakana, but in words often written in hiragana (native and Sino-Japanese vocabulary) and those in katakana (other loanwords and onomatopoeia). Mere rewriting hiragana ←→ katakana doesn't change the spelling.
The former way is mainly retained orthographically as reconfirmation of traditional convention. The original public notice on modern orthography clearly differentiates between pronunciation notation (ユー) and real spelling (ゆう).
ー appears in hiragana context indicating words or prolongation undefined in the orthography.
あーちゃん (a nickname), こんばんはー ("Eveniiiing!"), えー？ ("Gah!") cf. ええ ("Yes, sir/ma'am.")
While アイウエオ reduplication appears in katakana context representing syllable or pitch breaking.
アア溶岩 ("ʻAʻā lava"), サナア ("Sana'a", Yemen's capital), オオオオオオ ("Arghhhhh!", maybe a dying scream)
