People have often said that the Angel of Max Carnage requires more skill and game mastery than other challenge modes. The in-game description itself opens with "You hate chance,". However, in my experience an AoMC run involves a greater element of luck than standard play.
Why? Because AoMC eliminates only a single - and perhaps the least important - element of chance from DoomRL. In a standard run, thousands of shots can be fired. These will range from misses to max damage, but due to the very large number of rolls it is incredibly unlikely that on any given run you will give or take notably more or less damage than usual. In small situations a single roll can be important (eg. under fire from a mancubus), but these situations are uncommon enough that a player can reasonably predict and either avoid or recover from them.
By comparison, the mere existence of an invulnerability globe on a given level will make a much larger difference to the weapon damage given or taken. As these are rolled for only when a level is generated, there is also a much higher chance of abnormally many or few globes during a given run. In the extreme case, whether or not Hell's Armory appears can make a significant difference to a player's firepower - and this roll is made exactly once per run.
Fixing weapon damage in itself might shift the luck/skill balance slightly towards skill. However, by fixing the damage at maximum several other luck elements become much more important than normal. Let's look at the mancubus example again. In a standard game, the player can run behind a corner and kill it without risking much more than a large med pack. In AoMC, the same player with the same tactics risks instant death; the random chance being whether the mancubus moves or fires on the turn the player spots it. That one random roll now becomes much more important than the entire succession of rolls in a standard game!
Playing with high skill will reduce this. So would playing with high skill in a standard game, ergo the same player will be most influence by luck on AoMC regardless. The reasoning is fairly simple: Setting the damage high inevitably raises the consequences of other rolls, and sufficiently bad rolls can not average out over the game because, of course, the game ends when the consequences hit 'death'.
Conclusion: Sudden death is awesome, but there's a reason pro gaming tournaments don't start with it. :)