System differences
It's important to realize that there are significant differences between the PAL, NTSC and PC versions of the game (PAL is what you'll have for a European Xbox like mine, while NTSC is what you'll have in the U.S. and Canada). Because of this, some descent methods are practical for certain versions but problematic or plain impossible for others. For each descent method later, I'll give information on any system-related trouble as best I can so you can hopefully avoid disappointment, but my information for NTSC and PC is a bit sketchy in places and I have no experience of either, so if you have anything useful to contribute on that, I'd be very glad to hear from you. Anyway, here's some talk about some of the differences between the systems.
Longer falling on PAL
On PAL you can fall further than you can on NTSC and PC before the game kills you, and the same goes for falling covies I believe. While a PAL player can sail happily down to the snowy ledge from the bridge, to bounce off it or whatever, NTSC and PC players find themselves killed in mid-air before even reaching the darned thing, which must be pretty annoying. Longer falling is the main reason why there are so many more descent methods available to PAL players.
Greater landing resilience on PAL
On PAL, MC is considerably more resilient when it comes to landing a fall, compared to NTSC (and probably PC too). Impacts which are no trouble at all on PAL can be damaging or even life-threatening on NTSC. Impacts which are harsh but survivable on PAL are likely to be unsurvivable on NTSC.
Weaker traction on PAL
On PAL, it's like you have weaker traction than on NTSC and PC. This came to my attention when I was trying to do xbill's left ledge method, which can be seen nicely demonstrated on NTSC by Scurty in his YouTube video AotCR Bridge Fall Shortcut, plus AotCR Bridge Fall Shortcut (PC) for PC. When I hit that ledge I always slip off, no matter what I try. I just don't seem to have enough traction to slow myself in time. Nowhere near enough. I later found opinions in the High Speed Halo forum which seemed to echo the feeling that it was impossible on PAL (see here or here or here). Actually I've had a thought. Maybe this difference is due to MC's lower running speed on PAL. Perhaps I slide off that ledge because I can't run fast enough to counteract the slide quickly enough.
Weaker power of drift on PAL
On PAL you seem to have less power of drift than on NTSC and PC. I can't do the right cliff base method shown in Scurty's AotCR Bridge Fall Shortcut (2) video, because I can't drift towards the cliff base strongly enough. Scurty's NTSC power of drift looks way stronger than my PAL drift. Stronger drift is always going to be a help in making course corrections, and thus could be quite an advantage in helping you target particular spots when heading down for a landing or a bounce.
Slower running on PAL
Comparing some NTSC footage against my own, it seems that MC runs several percent faster on NTSC compared to PAL (in AOTCR at least). That could be relevant to certain descent methods for the following reason. If you're moving faster when running off a surface, you'll be able to travel further during the fall, which could help you reach desirable areas.
Slower weaponry on PAL
For at least some weapons, the NTSC/PC version is somewhat snappier compared to PAL, though this doesn't affect bridge descents of course. The pistol fires at a higher rate on automatic. The needler does likewise, getting through a clip in about 2 seconds compared to about 2.5 on PAL, and the needles travel faster too, all of which makes the needler seem practically turbo-charged compared to the PAL version I'm used to. Maybe there are differences in other weapons too, but these are the ones where I've really noticed it.
NTSC and PC almost identical?
I've not experienced Halo on these platforms myself, but according to BigGruntyThirst writing in the High Speed Halo forum, there's no significant difference between NTSC and PC. And since his thirst is both big and grunty, I'm prepared to believe him.
Why the differences between PAL and NTSC?
In a High Speed Halo thread Cody Miller offered an explanation for not being able to fall as far on NTSC compared to PAL. He suggests how the difference could arise from the frame rates at which the versions run; 25 fps for PAL and almost 30 fps for NTSC. His assumption is that the game makes checks once per frame. If that's correct, his explanation makes good sense. PAL is doing checks less often, and thus when you're falling, you're likely to be able to fall a bit further before a check comes along and decides you should be killed (killed because your downwards speed has reached or passed a certain kill-threshold). In his additional comment just a little further on, he points out how this would also mean less frequent checks for friction effects - which could explain why with PAL you can't stop yourself going off that ledge in xbill's method. I can imagine how the lower frequency could also result in PAL giving weaker drift. As well as all this, perhaps Bungie also tweaked some settings which happen to be relevant here?