You're neglecting the important detail in that Colossus-Slayer is the most abjectly boring option to pick from the available options. Sorry... it really is though.
In tabletop, I've found that the instances where you're taking your turn and you wish to ask "has that one been hurt yet", and the answer is no, comes up more frequently than individual impressions feel like, and conversely, the situations where you can get that extra free shot in because there are at least two enemies close to each other, happens fairly regularly - on account of melee creatures tending to try to attack the same targets, if nothing else.
Breaker is an entire extra shot, while Slayer is one extra fixed damage die on an existing shot; if you're getting them both every round, then your damage averages will be higher with horde-breaker overall. As long as one of your shots is against your marked target, hunter's mark is mostly irrelevant to the calculations, and no part of either feature has any bonus action requirements.
In a single target, boss-oriented situation, Slayer will naturally win out - if you are shooting boss and only the boss... but in major boss encounters, if you are the ranged damage-dealer, then there's a very high probability that add control is going to be your duty if and when minions show up - and if you're having to knock down minions before they can get to your casters or cause trouble, then they're mostly not going to be hurt when you first shoot them, so even in boss fights, as long as it's not a single thing with no support, Breaker still keeps up. If it is a single thing with no support, Slayer is definitely the way to go.
Let's suppose you're level 5, and run a few situations:
A group of small and medium size critters are assailing the group in a large space, but converging on your party - individually they aren't very tough, but there's a lot of them.
Breaker: marks the largest, toughest looking thing, and takes a shot at it (1d8 + 1d6 + 4); it dies - this is not a boss encounter. Is there a creature next to this one - let's suppose 'No'. Breaker looks around and takes their second shot against a minion that does have another minion next to it (1d8 + 4) x 2 - they kill 2 more critters. (Average turn damage: 29, 3 creature kills)
Slayer: marks the largest, toughest-looking thing and takes a shot at it (1d8 + 1d6 + 4); is the target hurt? Not when you shot, no bonus damage. It dies anyway, this is not a boss encounter. Slayers takes their second shot against another creature (1d8 + 4), and kills it too. (Average turn damage: 16.5, 2 creature kills)
This encounter continues with Breaker eliminating one additional monster on average per turn, until the encounter ends. Even if they don't always get their benefit, Breaker is still the more flexible and more effective option here.
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Suppose we add a boss creature to this though:
Breaker: marks the largest, toughest looking thing, and takes a shot at it (1d8 + 1d6 + 4); it's tougher than the others. Is there a creature next to this one - let's suppose 'No'. Breaker looks around and takes their second shot against a minion that does have another minion next to it (1d8 + 4) x 2 - they kill 2 more critters. (Average turn damage: 29, 2 creature kills, minor boss damage)
Slayer: marks the largest, toughest-looking thing and takes a shot at it (1d8 + 1d6 + 4); is the target hurt? Not when you shot, no bonus damage. Slayers takes their second shot against the boss creature (2d8 +1d6 + 4). (Average turn damage: 28.5, no add kills, but moderate boss damage)
Breaker still averaged higher overall damage and add cleanup. One could argue that the boss will drop sooner with Slayer, but if Slayer isn't controlling the minions, someone else has to instead, or they'll cause damage and interruption on the party.
Second turn:
Breaker: checks to see if there is a minion close to the boss - let's assume 'yes' this time, since we said 'no' last turn; Breaker can take both shots at the boss, and take their free shot at that minion: (2d8 +2d6 +8) + (1d8 +4) (Average turn damage: 32.5, 1 creature kills, moderate boss damage)
Slayer: Being generous and assuming the minions haven't caused any major issues or gotten close enough to make Slayer's shots difficult, they can take both shots at the boss (3d8 + 2d6 + 8) (Average turn damage: 28.5, no add kills, moderate boss damage).
Slayer still falls behind on average damage. All of Slayer's is on the boss target, while a portion (under 1/3) of Breaker's was on a minion.
Third turn:
(!) Let's suppose that Breaker's better add clean-up has removed the minions and provides no opportunity for their extra shot this round.
(!) Let's suppose that Slayer's extra boss damage will cause it to die on the first attack, but there are still minions.
Breaker: Only has the boss left, and takes both shots on it, but cannot gain their extra shot: (2d8 +2d6 +8) (Average damage: 24, boss dies, Encounter is complete!)
Slayer: Takes their first shot on the boss (2d8 +1d6 + 4), and it does. If we permit Slayer to re-mark between attacks (Formally, you should not be able to use a bonus action between the attacks of your extra attack, but *Most* DMs do permit this), they can then shoot one minion, (1d8 + 1d6 + 4) (Average Damage: 28.5, boss kill, 1 minion kill, Encounter is Not complete - 2 minions remain!)
Breaker: (Average Damage for encounter, 3 turns: 85.5, 3 minion kills, 1 boss kill. (!) Breaker's averages assume they did NOT get their perk on the third turn.
Slayer: (Average Damage for encounter, 3 turns: 85.5, 1 minion kill, 1 boss kill, Encounter incomplete - minions remain. (!) Slayer did the same damage every turn, and their average assumes they Did get their bonus every turn.
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Lastly, let's assume the party is attacked by a single powerful entity, with no support:
Breaker: Marks the boss and takes 2 shots: (2d8 + 2d6 + 8) (Average Damage: 24)
Slayer: Marks the boss and takes 2 shots: (3d8 + 2d6 + 8) (Average Damage: 29.5)
Slayer doesn't get their bonus on the first shot, but they get it on the second shot of that same first turn, so they do get it every round. In this scenario, nothing changes, all numbers are consistent and continue, and Slayer averages more damage to the boss target by a few points (4.5, average of 1d8) each round. Slayer comes out on top in situations where they Always get their benefit and Breaker Never gets their... this should not surprise anyone. Conversely, Slayer remains the better and more interesting choice in situations where both get their perks consistently, and even in cases where slayer always gets theirs, and Breaker only gets theirs some of the time. If slayer focuses on getting the most damage they can every round, they'll also end up neglecting other elements of more complex fights, and leave those tasks to others and potentially drawing out a fight that they sought to speed up.
