This is a difficult one. My own suggestion for a General Purpose Cartridge (GPC) as developed in detail HERE concerned one which could replace both the 5.56 mm and 7.62 mm NATO rounds with one intermediate in power between the two of around 6.5 mm or 6.8 mm calibre, using relatively low-drag bullets to deliver long-range performance to at least match 7.62 mm, while having significantly less weight and recoil than that cartridge.
To put some numbers on that: the 5.56 mm develops around 1,700 J muzzle energy, the 7.62 mm some 3,400 J, and my GPC around 2,500 J.
I should maybe emphasise that the 6.8 mm Rem SPC is less powerful than my GPC and handicapped by only having room to fit short, high-drag bullets, harming long-range performance, so it cannot be a GPC. The 6.5 mm Grendel is better, although still not quite powerful enough IMO.
The .264 and .277 USA (6.5 mm and 6.8 mm respectively) developed by the US Army Marksmanship Unit (USAMU) several years ago initially matched my proposals quite closely. However, they subsequently uploaded the case to improve the performance, at the cost of more recoil and less controllability in burst rifle fire.
More recently, the Army has changed its ammunition performance requirements to include the ability to penetrate modern military-grade body armour at normal combat distances. This requires a lot more power than my GPC, with a muzzle energy significantly higher than even 7.62 mm - in the region of 4,000 J. In 6.8 mm calibre as specified by the Army, this is really in the magnum class.
To make matters worse, the Army not only wants to use this in MGs, but also in compact carbines. In conventional weapons, that means a short barrel, and the shorter the barrel, the higher the chamber pressure needs to be to achieve any given muzzle velocity. So all three competing cartridges are apparently running much higher pressures than existing military ammunition. There are obviously risks in this approach, and high pressures mean greater barrel heating and wear as well as more risk of things breaking.
I personally like the GD-OTS weapons using the TV ammo, for three reasons:
The compact bullpup carbine layout permits a long barrel in a short gun (there’s about an 8 inch length saving over a conventional rifle), also helpful because of the requirement to use a suppressor, which adds more weight and length.
The longer barrel means that the pressure can be lower for the same performance.
The polymer case has an insulating effect, so the chamber will not heat up so quickly and cook-offs are difficult to achieve. There is also a greater weight saving than the metal-cased SIG. Of course, that assumes that the polymer is able to meet exacting military standards.
However, none of these cartridges is really a GPC in my opinion; if the Army does adopt one of them, it would probably only be issued to front-line infantry whose primary weapon is the rifle. There would still be a need for something much smaller, lighter and handier for all other troops, so the 5.56 mm M4 would probably remain in service (in much larger numbers than the 6.8 mm) for the foreseeable future.