Which is bigger - the Star Forge, or the Death Star?

If you've played Star Wars: Knights of the Old Republic, you're familiar with the Star Forge:

I haven't found any definitive information regarding the size of the Star Forge, but I know that the conservative estimates for the sizes of the Death Stars are 120 km diameter and 160 km diameter respectively.

Estimates for the Star Forge itself vary DRAMATICALLY:

Star Forge Diameter = 91 kilometers

Star Forge Height = 272 kilometers
- Source

And:

Star Forge Diameter = 11 kilometers

Star Forge Height = 28 kilometers
- Source

I think SF&F can do better than this.

Assuming that these estimates of the Death Stars' sizes are correct, which is bigger? The Star Forge, or the Death Star?

Answer

Based on the information given in the question concerning the specs of the Death Star, its radius is no smaller than 60,000 m, which gives a volume of 9.05 x 10¹⁴ m³.

Now, here is the Star Forge:

Based on this information about Hammerheads supplied by the OP,

(in particular that the length of the Hammerhead is 315 m), and based on this video also supplied by the OP,

I used some frames when the Hammerheads are between the fins of the Star Forge to give an upper bound on the diameter of the spherical part of the Star Forge as being at most 20 Hammerheads, which works out to a maximum radius of 3150 m. This gives a volume of 1.31 x 10¹¹ m³ for the spherical part.

Now, there are six fins on the Star Forge, three on top and three on the bottom. Now, let's say that each fin has twice the volume of the sphere, which is a gross overestimate, given how thin they are. That would make the total estimated volume of the Star Forge thirteen times the volume of the central sphere, which is roughly 1.7 x 10¹² m³.

This still makes the Death Star a whopping 530 times more voluminous than the Star Forge (9.05 x 10¹⁴ divided by 1.7 x 10¹²).

Even if I make the radius 20 Hammerheads (instead of a diameter of 20 Hammerheads) — which is another gross overestimate on the Star Forge — I still get that the Death Star is bigger, but only by about 65 times.

Another Way to Compare: If we suppose that the Star Forge were a sphere, with radius from the center to the end of the longest fin, that would be about 60 Hammerheads — but let's say 80 to overestimate. This gives a radius of 25,200 m, which is still less than half the radius of the Death Star (and makes the Death Star about 15 times the volume of this sphere), and the actual volume of the Star Forge would be much less than that of this pretend sphere.