Overall it's better to ask for permission, but it does depend on the situation. You ma end up doing something that doesn't require permission but screw up and involve something else like braking something ect and then you'd need to ask for forgivness. If you look at the case of which is better, to ask permission before you do something that requires it, or ado it anyway and ask for forgivness after then I'd still say you should ask for permision.
The extremes would be, you ask for permission every time, you win some you lose some, you get a good reputation for being dependable. You never ask for permission but you always do it anyway, you always ask for forgivness afterwards, you end up in trouble and with a reputation for not being dependable, you risk it coming back at you when you want someone to do something or other people start treating you the same way.
