While I accidentally selected the Trench Gun for the poll, I really would have to say it is dependent on the map and flow of the game I'm in. After serious thought, I actually find that the Thompson is one of the best options as an Allied SL.
I personally would have to say that the Thompson is one of the best options you can select as a SL purely on the reason that most engagements happen under 100m which is an effective range for the Thompson. In strict comparison to the M1 Carbine & the Trench Gun, the Thompson also allows you to pour more rounds faster into enemy players (increasing kill/wound potential before the enemy is out of sight/in cover) especially if they are banzai'ing, flanking, or rushing from cover to cover. It has a more than adequate ammo capacity per magazine (which gets even better once you unlock the drum magazine at L50) and it allows you to defend yourself very effectively if enemies try to rush into your position to overwhelm you.
In regards to the M1 Carbine, I personally enjoy using this weapon as well but for the reasons I prefer the Thompson, the M1 Carbine is simply outclassed. The M1 Carbine has a reasonable ammunition capacity for magazines but low kill potential per shot (sans lethal hit areas; head, etc.) but fires at a slower rate than the Thompson. This lower firing rate coupled with low kill potential per shot means that if you get rushed by 2+ enemies in close quarters it is likely that you will find yourself gunned down or run through by a bayonet. In comparison, the M1 Carbine has significantly higher accuracy compared to the Thompson, especially at range, but that leads me to my next point.
If your focus is remaining as a mobile spawn point for your squad when attacking/defending, you likely won't be taking pot-shots at your enemy as much as a Rifleman or BAR-user would; to do so would be to risk possible death from an astute rifleman. In general, I've found it far better to remain in cover and watch the flanks to support your squad whilst they directly engage the enemy. While you could get an M1 Carbine and try to kill entrenched enemies, the risk outweighs the reward in most scenarios. If it is a long distance map or you are in a section with limited cover (open fields of fire), the M1 Carbine may make more sense than the other two options, though. In fact, if your goal is to support your team by watching the flanks, the M1 Carbine or Thompson are both viable options as they both have good potential when being defensive/"safe" about advancing- the Thompson is the clear winner when it comes to assaulting an objective or area with your team though for the aforementioned reasons.
For the Trench Gun, I've had hit-or-miss luck with it. There have been times where four center mass shots did nothing to an enemy that was <10m away who wasn't banzai'ing and there have been times where I've managed to take down four Banzai'ing Japanese at 20m with three shots. I would say the Thompson overlaps with the Trench Gun in some areas and in some regards outclasses them. For general utility, the Thompson is a far superior choice. However, I will say that the Trench Gun does feel rather satisfying to use when an enemy turns a corner right into a blast from it or when you drop into a trench and start blasting away at those inside of the trench.
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