Wil, historical quarterstaff techniques appear to include treating both ends of the staff as identical. Which, of course, they are. And which greatswords most certainly are not.
Hans
Actual quarterstaff isn't always identical ends - the important aspect in the manuals (period and non) is that the quarterstaff techniques involve striking with ends from a central grip. A technique that is in several period bastard sword and greatsword manuals, as well. (The non-identical ends is an issue of wear and source-wood. Quarterstaff, historically, was field-crafted.)
Quarterstaff skill can readily be used with spears; a slight bit more thought required for polearms other than spears (Polemaces are just off-center for quarterstaff; poleaxes require slightly more care not to catch the head on self). Greatswords are used in a variety of ways, and there is little loss to a staff-technique from hitting with quillons, hilt or flat - there is much to be gained by edge-hit from the blade.
The overall mass and lengths are comparable, and the staff techniques can be done with a typical historical blade of that size.
A blade is a force concentration tool - no near-modern army (including marine armies) has ever had a successful campaign without bladed weapons, if only for their utility uses. A greatsword can be used quite effectively to chop trees. An axe is better - more mass-moment, more wood removed per strike.
A bayonet is useful for cooking, carving, and (in a pinch) digging, as well as being a way to have a spear without carrying a spear.
A pick is better against armored targets than a sword - but a sword can do better than a staff in most cases.
Marines with greatswords is a bit farfetched - but a "modern cutlass" of the mamluke-hilted shamsheer type carried by USMC was a practical blade - enough mass for practical combat, curved makes it easier to wield in the confines of a ship, and the gentle curve means thrusting techniques DO work nicely. (I've fenced using and against a rebated shamsheer - it's actually harder to defend against its thrusts than against a rapier!)
Likewise, staff aboard ship is going to be short staff for the same reasons as cutlasses instead of greatswords...
... space and damage to equipment.
The only reasons to prefer melee weapons are that of preserving the ship. Firearms will result in damage to consoles, displays, etc. Even a hit will usually overpenetrate and thus go through the target into systemry.
Melee weapons suffer this far less... having fenced in close quarters (rapiers in hallway), no significant damage to the breakables at the ends occured - even a single BB gun miss would have damaged them.
Which brings back to discussion of roles.
The role of Naval infantry is dismounted/ashore - as is that of marines - but ship's troops may include standing anti-boarding teams, who, for the very same reasons as the naval infantry, will be drawn from the same pools of persons.
Repelling boarders, you want shotguns, snub pistols, and melee weapons. You want melee weapons easily wielded in ship's corridors, both for practice and practical application. You want the snub and shotgun because they will not overpenetrate the target, and because in areas without instrumentation, they are highly effective, misses don't go through the walls, and they still can injure effectively against unarmored targets.
The period greatsword techniques included strikes to unarmored locations, as well - so the traveller "broadsword" (A bastard sword or smallish greatsword) is likely to be seen as a melee weapon for battledress troops - because it's one of the few massive enough to break through the weak spots, and agile enough to hit them. (The techniques for which parallel center-and-end grip staff trip techniques for tripping; grip on the blade just below the false quillons, and lever with hand on the hilt to bring the tip into the back of the knee...)
Using advanced metallurgy, I can see greatswords used to take out BD and CA troops, both in boarding actions and ashore. (I can see staff, or spear, or broomhandle being used for the exact same strikes, but with less permanent results.... the strike mode is the same for all 4 weapons, including how the levering is done.) So I can see it being an available training for NI and Marines, and the weapon being elective carry. (3I marines don't - cutlass tradition leads to standardization - but that 8+ roll is better explained by "you've got the stupid thing on your hip 90% of the time.")
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...some wit (or half) is going to take the bait and answer it 
