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I prefer being able to allocate points as I see fit (that's also my favoured approach for tabletop roleplaying games). You might want to place certain restrictions (eg perhaps each player can only have one 'super stat', and maybe there are minimums for certain stats), but overall I think it's nice to allow that sort of customisation.
Randomisation can work okay if implemented in a balanced way - for example, if everyone has exactly the same stat total, but their individual stats are distributed randomly based on certain criteria, with each stat being of equal value.
The "roll 3d6 for each stat" approach tends to result in people rolling, and rolling, and rolling, until they get decent stats. I've seen muds which didn't reveal this information until a certain level, and that simply resulted in the hardcore players creating and discarding characters until they got what they wanted.
Even if you were able to stop people scrapping and rerolling characters, you'd still end up with situations where some players get "lucky" starting characters and others get really bad ones (even in an application-based system, such characters are likely to have "unfortunate accidents" so that the player can reroll).
Aside from min/maxing, some stat randomisation systems will also blocking people from playing the sort of character they want to play. If you roll a strength of 3, then you're going to have to revise your "exiled knight" idea. Intelligence 3 as well? There goes that "eccentric Alchemist" concept. Charisma 3? Goodbye "corrupt politician" concept. Even many hardcore roleplayers are going to be put off if they log on to your game and find that the only character type they qualify for is "village idiot" (it might be amusing for a short while, but the novelty would soon wear off).
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