Sphere
Needs to figure out, what spherical shape good for.
Atmosphere landing - not so good, but less surface to cool, bigger volume for coolant, less material(mass) of craft, ability to rotate surface for even heat distribution, there is something to think about.
One of good things is: Maximum volume with minimum surface(and mass as result).
First of all, you have to need that volume, for some reason.
Less surface, means less mass of construction, which is always good for spaceship, if it uses reactive propulsion. And this is pretty universal reason to have spherical form, but how much it affects on decision of choose spherical form, depends on: our goals, needs, which possibility's we have to implement our wishes, etc.
So talking about form, prior to define all of that, is bad idea.
Spherical form is good for space and space ship, not so good for landing on Earth or planets with atmosphere.
Let assume we have plenty activities to do in space.
Good
- Less surface
- less craft mass
- less surface repairs
- less material for radiation protection.
- Spherical form
- there no defined axis of symmetry (indefinite numbers of them). It means no preferred direction for micrometeorites to hit from, all directions kinda equal, in therms of impact results. That good in case if there no preferred direction for them to come from, if they intended to destroy ship. Projection is same from different angles.
- less inertia momentum, good for maneuvers
- Volume
- recreation
- industry
- ship repair capability (may place all needed equipment, just in case, and use if needed)
- volume to place reactors or energy sources, shields if needed.
- food production
- waste utilization
- size of crew personal volume
- artificial gravity (cylinder is better though, less tech needed)
- more equipment for mission, which may be used at arrival.
- Propulsion system + Spherical form + maneuvering
Main propulsion system may be attached on surface of that sphere and may be movable. It means that we don't need to have extra engines to maneuver and no need to spend much energy or reactive mass to fight inertia momentum of the main part of the ship. Which may be big, huge, in case if it transports much hydrogen, for mars terraforming(as example)
Construction
You may or may not to be able build ship in space.
If not, if you can't, there is not much to choose. Almost everything depends on your capabilities to carry payload to orbit. You fit that construction to satisfy payload requirements. Is that BEAM or anything else.
If you can build construction in space, there is not much difference between cube, sphere, cylinder. In therms of building, at least.
Heat dissipation
One thing people constantly mention, and usually they mention it as stop factor, without defining some circumstances, which are important in that topic.
$$
\frac{Radiative Power}{Surface Area}=j=\sigma T^{4}
$$
$$
\sigma=\frac{2\pi^5 k^4}{15c^2h^3}= 5.670373 \times 10^{-8}\, \mathrm{W\, m^{-2}K^{-4}}
$$
$T=100K, j \approx 5.7W/m^2$
$T=200K, j \approx 91W/m^2$ ISS uses NH3, near freezing for it, with normal pressure
$T=240K, j \approx 188W/m^2$ ISS NH3 boiling point, with normal pressure
$T=300K, j \approx 460W/m^2$ Kinda room temperature
$T=336K, j \approx 726W/m^2$ Temperature of thin sheet heated by Sun on earth orbit
$T=400K, j \approx 1452W/m^2$ Something thick with low heat conductivity, surface temperature
$T=823K, j \approx 26014W/m^2$ 550 Celsius, Steam in steam turbines
$T=1273K, j \approx 149kW/m^2$ 1000 Celsius
$T=1773K, j \approx 560kW/m^2$ 1500 Celsius, Some cobalt based cutting tools work even that hot
It is Very important to understand what $T^4$ means, to have grasp how fast it grows, it makes big difference in efficiency.
It is also important, how energy is generated. Because of $T^4$ it is even more important then heat dissipation in space.
As example if solar will work, when all it part are at temperature 400K (is doable) then using that energy, you pretty easy may have $823K, 26014W/m^2$ dissipation from surface of the ship.
Living volume as heat source
Let say there is 50kW heat sources per capita, volume 1000 $m^3$ per capita(food growing, living rooms, storages, service rooms etc), and heat dissipation $5kW/m^2$ (ca 270 Celsius ship surface temperature, not big problem, if there is energy), with 50% efficiency of cooling system - this ship may be 250 meters in diameter.
10 by 10 by 10 meters minus all service etc stuff - not to much room to live, not so pleasant.
Same as above and 10000 $m^3$ per capita - ship may be 2500 meters in diameter.
In such cases there will be equilibrium between Radiative heat dissipation and needs in that dissipation.(less diameter and it will loose heat faster then it is generated)
So ship may be pretty big.
If that ship have to transport some goods, resources etc - living volume would be fraction of it's volume, so even ISS approach may work well, just using surface of ship.
Engines as heat source
Depends on engines, on their efficiency. Current engines handle that issue, and no reasons to think oppositely. Current engines are pretty efficient. But that is not much connected with ship shape. Good thing there is no need to place there engines inside ship, with spherical ship it even better to be outside.