Does the Hellkite Drake behave differently on XBox 360 compared to on PC?

I am playing Dark Souls on the XBox 360 (patch 1.06).

For me the Hellkite Drake attacks almost immediately when I step onto the bridge. I have never made it to the stairs without getting burned once.

I’ve been watching a play-through of the game on YouTube and the player seems to be able to walk around freely on the first half of the bridge. The drake doesn’t seem to attack at all until he reaches the stairs. Even when he wanders around on the second half of the bridge, the drake seems to attack a lot less often than I have come to expect.

The only difference I can see between me and him is that I’m playing on the XBox 360 and he’s playing on PC. Is there some difference in the behaviour of the drake between platforms?

Edit: This is the video I’m referring to:

I now realise that the difference is partially explained by the fact that the player is crossing the bridge for the first time, and that the Drake is less aggressive when the player has not yet rested at the bonfire.

The player does get burned on the initial fly in, but then he walks around quite freely without getting attacked again. I think the Drake kept attacking me multiple times on my first crossing. I have done this section of the game a couple of times with two different characters, but I might be misremembering.

Here is a later point in the same playthrough:

Here the Drake is more aggressive than before but still less aggressive than I was expecting. I find that I barely have time to run from the stairs to the safe point, but in the video the player is able to make it with time to spare.

About a minute later:

My jaw hit the floor when I saw this. There is way more time to cross the bridge and run past the Drake than I was expecting. The first time I passed the Drake I got caught in multiple attacks and I don’t think I would have survived without Flash Sweat.

At this point I am prepared to believe that I am perceiving an illusory difference, due to the change in my psychology when watching the game being played compared to playing it myself. I’m interested if people have further observations, though.

I also realise that my original description doesn’t really match what happens in the video, so I’m not sure where that discrepancy came from. It’s possible there are other relevant sections in the playthrough that I’ve missed out here.

Edit 2: I also just noticed that the player takes way more damage when he is hit by flames while sprinting, compared to when he is just walking. Looking back, I think maybe I always instinctively tried to sprint away when the Drake attacked, and that may have caused me to take more damage, creating the perception in my mind that the Drake is more dangerous than it actually is. Perhaps I need to learn to not do that? :-)