Praying at 3am houldn'g make any difference. Far as I know, you can pray any time you like or perhaps 3am is more quieter for you so you can concentrate then thats fine, otherwise its more by choice and the time you have. Some people work at nights, and this might be the only time they can pray.
The reason it is so powerful is because that is the time that Christ died. Therefore, when praying at this specific time, it holds much more meaning.