Another one is the banlist.
Standard, Extended and Legacy have a banlist. If a card is too powerful, WotC excludes it completely from the format.
Vintage has a restricted list (and a short banlist with ante-cards and some exceptions, but not because the cards are too powerful), they still let you play at least 1 copy of every black-/white-bordered card printed since 1993 in your deck.
The only other difference I can think of is that in Vintage and Legacy, the decks that are used are pretty static, when in standard, 'net decks' are dynamic, with each new set bringing cards that add to certain decks, cards that hose certain decks and new combo's to the table