...but I haven't managed to find them anywhere, even with Search, so...
I recall a topic where a couple of players (capn233 and Drayce333 I think) argued about whether Marksman or Adrenaline Rush was better...
I think it was some sort of bonus power thread.
Anyway I guess I will answer the questions as far as my preference:
*If you are into theorycrafting, Marksman will give better DPS with most automatics than Adrenaline Rush. You could consider the ROF bonus a "multiplicative" damage bonus. Adrenaline Rush has a mediocre additive weapon damage bonus, but it is better than nothing. Marksman does not increase stability (neither does ARush for that matter).
*As above, you can use Marksman under Tactical Cloak, which was a blunder in game design. You cannot use it under Adrenaline Rush since the "Bonus Power" evolution of ARush specifies an "offensive power" which is another way of saying "direct damage power."
*Infiltrator should do better pure weapon damage than a Soldier. Soldier will do a whole lot more ammo damage when you take Incendiary Explosive Burst and pair it with a high ROF weapon. Infiltrator can probably make it up if he takes James or Marksman.
*Infiltrator has two different base damage modifiers for sniper rifles ("multiplicative bonuses"), TacCloak Rank 6 and SR Damage in passive. The only thing that can keep Soldier somewhat competitive is ARush's free reload.
*A lot of people act like the Saber requires Marksman to be decent in MP, but I am not one of those people. If you recognize that you cannot fire it at max ROF against smaller targets, it is fine. The main benefit of Marksman with the Saber in my mind is damage vs large targets. In SP I do not use the Saber as much on Soldier as I do on the HSoldier in MP largely because the best configuration is Extended Mag, Extended Barrel and AP ammo. If you run Marksman in SP on a Soldier to use the Saber, you will want to run a Mag / Piercing combo. I don't know if that will lead to requiring extra headshots or not.
*If it wasn't pointed out, or you didn't realize it, Marksman in SP never gained the free reload when you activate it. This is a major reason why in practice I do not feel like it offers a lot of benefit over Adrenaline Rush in SP.
*You can't fire an offensive power under Marksman, which is Adrenaline Rush's biggest advantage (or second biggest advantage behind free reload). If you care to make up the damage with ARush, you can do so by taking Proximity Mine as the bonus with Damage Taken and fire it with each Adrenaline Rush cycle. You still will not have as good stat DPS, but I don't think the killing speed difference is significant enough in SP given their lower HP pools relative to Gold MP.
*There are several weapons I would almost never consider for Marksman over Adrenaline Rush in SP. Mostly weapons where magazine size is limited and they either already do significant damage, have high accuracy, and or are semiautomatic with good rates of fire to begin with (click speed limited). The one exception that may seem to fit those criteria, but is absurd under Marksman, is the Raider.
Anyway in a vacuum it is hard to recommend one over the other. My point of view is that Marksman isn't worth taking on the Soldier in SP unless you are simply taking it for the sake of running a Marksman Soldier. I do not find a lot of utility in trying to find the absolute maximum stat DPS build since SP is much more skewed towards trash mobs.