The main difference between normal and Vintage items is that Vintage items are all the items people obtained before the Mann-conomy update. They can no longer be acquired in any way except trade. This makes them very rare. You can recognise them by their blue name only, since people could also just rename their items Vintage. Also, as pointed out in the comments, the "Vintage Tyrolean" and the "Vintage Merryweather" are renamed to "Vintage Vintage Tyrolean" and "Vintage Vintage Merryweather" respectively.
See the Mann-conomy FAQ:
Q: Why have all my items switched to "Vintage" items?
A: Some items that used to be rare will become more common when they are available for purchase. We wanted to give players this option, but still recognize people who obtained those items “the old-fashioned way” in the past. So we decided to perform a one-time conversion of all the old items into "Vintage" versions, which will never be attainable in the future. This way, those older rare items remain rare (in fact, they're even rarer, because they're limited editions now).
Basically, Valve decided that making items available for money devalued the items, since it is less impressive to buy an item then it is to craft/find it. Therefore they converted every existing item in people's inventories to Vintage items.
Since you can no longer create them (only the items converted at the update become them) Vintage items are very rare, which gives them a higher value in trade. Otherwise they are identical.
Additionally, a couple items are excluded, such as badges, promotional items (eg. Bill's Hat) and holiday items (eg. Ghastly Gibus).
Funnily enough, the Vintage item's rarity will increase over time, as people use them up in crafting.
See also: The Quality article on the Team Fortress wiki.
According to an interesting forum post describing the advantage of the degreaser, the default switch time is 0.67 seconds.
As far as I know only the Degreaser (65% faster, 0.67(1-0.65) = 0.2345 seconds) and Reserve Shooter (15% faster, 0.67(1-0.15) = 0.5695 seconds) can affect this, besides the weapon-specific limitations as mentioned in Toomai's answer. Also of course the Half-Zatoichi is 'honorbound' and has a switch time as long as it takes you to get a kill!
Best Answer
The Witching Hour is an event that happens every now and then where the clock tower beyond the pit of Helltower rings. When it does, two etheral paths temporarily appear so players can walk across the pit and reach the base of the clock tower, where they can collect a rare spell and warp back to their spawnroom with a speed and health buff. Getting a rare spell in this way earns an achievement.