I agree with those who say it should remain being rolled at the start of the creatures turn.
Rolling at the end of the turn means letting the players know what the monster will do on its next turn. If the dragon recharges its breath, they know to spread out so it can't hurt them. This decreases the tension, because there is no unknown element.
Rolling at the start of the turn gives the players something to hold their breath for. Better yet, if they don't know whether its powers are recharge or not, they will have to plan for every possibility they've witnessed, because they don't know if it could happen next turn (if it's at-will), in a few turns (if it's rechargeable), or never again (if it's encounter). That's what raises the tension: mystery.
This is the reason DMs use screens. If the players don't know what they monsters roll, then the DM can milk that. He rolls the dice, the players hold their breath. The DM looks up. "The evil paladin raises his sword, directing at Tanya, who only has 2 hp left." The wizard gulps. This could be the end of her character. The DM continues, "He swings! Tanya leaps to the side, but the sword is fast. It slashes right through her robes..." The player is beginning to moan, looking to make sure she has enough for a raise dead ritual, when the DM finishes, "missing her entirely." The player looks up, a smile spreading on her face. "She has escaped his blade!"
Of course, this is only effective maybe twice an encounter, when it really starts to get gritty for the characters. However, if you are rolling behind a screen anyway, then the characters don't know whether you roll at the start or the end of the monster's turn! In this case, you still probably want to roll at the start of the turn, for the aforementioned bookkeeping reasons. Would you rather remember if you used the power before (which should be easy if it's a memorable enough power) or what you rolled for recharge (which is a 1 in 6 random number, not at all memorable)?
However, if you find that end of turn works, all the better for you. Do what's fun in your game.